SAT Function Notation Practice Questions | Download PDF

Correct answer: A, f(5) equals 13.

Substitute 5 in place of x: f(5) equals 4 times 5 minus 7, which equals 20 minus 7, which equals 13.

Answer B, 20, is what you get if you compute 4 times 5 and stop without subtracting the 7. Always carry the entire function rule through to the end before writing your answer. The most common basic evaluation error is treating one part of the expression as the full answer.

Correct answer: B, g(4) equals 26.

Substitute 4 for x: g(4) equals 4 squared plus 3 times 4 minus 2.

That is 16 plus 12 minus 2, which equals 26.

Answer A, 22, comes from computing 4 plus 12 minus 2, treating 4 squared as just 4 rather than 16. Always square the substituted value before adding the other terms. Order of operations applies inside function evaluations exactly as it does in any algebraic expression.

Correct answer: C, h(negative 3) equals 13.

Substitute negative 3 for x: h(negative 3) equals 2 times (negative 3) squared minus 5.

(negative 3) squared equals 9. So 2 times 9 minus 5 equals 18 minus 5, which equals 13.

Answer A, negative 23, comes from treating (negative 3) squared as negative 9, which is wrong. Squaring a negative number always produces a positive result. (negative 3) squared is positive 9, not negative 9. When a negative number is the input, use parentheses around the entire substituted value to keep the sign handling clear.

Correct answer: B, p(7) equals 46.

Substitute 7 for n: p(7) equals 5 times 7 plus 11, which equals 35 plus 11, which equals 46.

This question uses n instead of x as the variable inside the function. The SAT does this regularly to test whether students understand that the variable name is just a placeholder. The evaluation process is identical regardless of which letter names the input.

Correct answer: C, f(0) plus f(2) equals 6.

f(0) equals 3 times 0 squared minus 4 times 0 plus 1, which equals 0 minus 0 plus 1, equal to 1.

f(2) equals 3 times 2 squared minus 4 times 2 plus 1, which equals 3 times 4 minus 8 plus 1, equal to 12 minus 8 plus 1, equal to 5.

f(0) plus f(2) equals 1 plus 5, which is 6.

Questions asking for combinations like f(0) plus f(2) require two separate evaluations before any addition. Never try to combine the inputs first. f(0 plus 2) is not the same as f(0) plus f(2), and the SAT sometimes includes the combined version as a wrong answer choice.

Correct answer: A, x equals 1 and x equals 5.

Set the function equal to zero: negative x squared plus 6x minus 5 equals 0.

Multiply through by negative 1: x squared minus 6x plus 5 equals 0.

Factor: (x minus 1)(x minus 5) equals 0, so x equals 1 or x equals 5.

Both are positive values, so both are valid answers.

When a question asks for values where f(x) equals zero, it is asking for the x-intercepts of the function graph. Setting the function rule equal to zero and solving by factoring is the algebraic version of the same process. In Desmos on test day, you can graph the function and click both x-intercepts to read these values directly.

Correct answer: C, r(3) equals 12.5.

Substitute t equals 3: r(3) equals 100 times (0.5) to the power of 3.

(0.5) to the power of 3 equals 0.5 times 0.5 times 0.5, which equals 0.125.

100 times 0.125 equals 12.5.

Exponential functions appear frequently in SAT function notation questions. The base (0.5 here) is raised to the power of the input. A common error is multiplying the base by t rather than raising it to the power of t. 100 times 0.5 times 3 equals 150, which does not even match a choice, but is the kind of mechanical substitution error that happens when a student does not recognize exponential form.

Correct answer: B, x plus 3.

Factor the numerator: x squared minus 9 equals (x minus 3)(x plus 3).

Divide by (x minus 3): the (x minus 3) factors cancel for all x not equal to 3, leaving x plus 3.

This is a rational function simplification question using function notation. The key is recognizing the difference of squares in the numerator. x squared minus 9 equals (x minus 3)(x plus 3), which is a factoring pattern worth having automatic on test day. After cancellation, the simplified form is x plus 3, valid for all x except x equals 3.

Correct answer: C, k equals 5.

Substitute x equals 3 and set equal to 0: 3 squared minus k times 3 plus 12 equals 0.

9 minus 3k plus 12 equals 0

21 minus 3k equals 0

3k equals 21, so k equals 7.

The verified answer is k equals 7, which is answer D. This type of question gives you an output value and asks you to find an unknown constant in the function rule rather than the input value. The substitution process is identical to normal evaluation, but after substituting you solve for k rather than finishing the arithmetic for a numeric output.

Answer: 20

Substitute negative 2 for x: f(negative 2) equals 3 times (negative 2) squared minus 2 times (negative 2) plus 4.

(negative 2) squared equals 4. So 3 times 4 equals 12.

Negative 2 times (negative 2) equals positive 4. So minus 2 times (negative 2) equals plus 4.

12 plus 4 plus 4 equals 20.

Write out the substitution with parentheses around the entire negative value before simplifying. f(negative 2) equals 3 times (negative 2) squared minus 2 times (negative 2) plus 4. This keeps every sign visible and reduces the chance of a negative-squared error.

Correct answer: B, 3x plus 11.

Replace every x in the rule with the expression (x plus 4).

f(x plus 4) equals 3 times (x plus 4) minus 1, which equals 3x plus 12 minus 1, which equals 3x plus 11.

Answer A, 3x plus 4, is what you get if you treat the 4 as the only new piece rather than substituting the entire expression (x plus 4) into the rule. The full expression goes in wherever x was. Distribute 3 across both terms of the input expression before combining the constants.

Correct answer: B, 9t squared plus 2.

Replace x with 3t: g(3t) equals (3t) squared plus 2.

(3t) squared equals 9t squared. So g(3t) equals 9t squared plus 2.

Answer A, 3t squared plus 2, is what you get if you only square the t but not the 3. When an expression is placed in the squared position, you must square the entire expression. (3t) squared means 3 squared times t squared, which is 9t squared. The 3 and the t are both squared.

Correct answer: A, 2a squared plus a minus 1.

Replace x with (a plus 1): f(a plus 1) equals 2 times (a plus 1) squared minus 3 times (a plus 1).

(a plus 1) squared equals a squared plus 2a plus 1.

So 2 times (a squared plus 2a plus 1) equals 2a squared plus 4a plus 2.

3 times (a plus 1) equals 3a plus 3.

f(a plus 1) equals 2a squared plus 4a plus 2 minus 3a minus 3, which equals 2a squared plus a minus 1.

When the expression input contains a plus or minus, be especially careful expanding the squared term. (a plus 1) squared is not a squared plus 1. The full expansion using FOIL or the perfect square formula gives a squared plus 2a plus 1. Missing the middle term is the most common algebraic error in this skill type.

Correct answer: A, negative k.

h(2k) equals 5 minus 2k.

h(k) equals 5 minus k.

h(2k) minus h(k) equals (5 minus 2k) minus (5 minus k), which equals 5 minus 2k minus 5 plus k, which equals negative k.

When subtracting a function value, distribute the subtraction sign across every term of the second expression. (5 minus 2k) minus (5 minus k) requires distributing the negative sign through the parentheses, changing (5 minus k) to (negative 5 plus k). Students who forget this step get a wrong answer by leaving the signs of the second group unchanged.

Correct answer: A, negative 12.

f(x minus 3) equals 4 times (x minus 3) plus 7, which equals 4x minus 12 plus 7, which equals 4x minus 5.

f(x) equals 4x plus 7.

f(x minus 3) minus f(x) equals (4x minus 5) minus (4x plus 7), which equals 4x minus 5 minus 4x minus 7, which equals negative 12.

The x terms cancel in this difference, which is actually a useful check. If you are finding the difference between two evaluations of the same linear function at inputs that differ by a constant, the x terms will always cancel and you will always get a number. That pattern tells you the answer should be a clean number, not an expression involving x.

Correct answer: C, m equals 5.

Set the function rule equal to 29: m squared plus 4 equals 29.

m squared equals 25, so m equals 5 or m equals negative 5.

Since the question asks for a possible value and 5 is among the choices, m equals 5.

The phrase a possible value signals that there may be more than one correct value. Here both 5 and negative 5 satisfy the equation, but only 5 appears as an answer choice. On a student produced response version of this question, entering either 5 or negative 5 would be accepted.

Correct answer: A, 4x squared plus 4x.

Replace x with (2x plus 1): f(2x plus 1) equals (2x plus 1) squared minus 1.

(2x plus 1) squared equals 4x squared plus 4x plus 1.

Subtract 1: 4x squared plus 4x plus 1 minus 1, which equals 4x squared plus 4x.

The key step is correctly expanding (2x plus 1) squared using the pattern (a plus b) squared equals a squared plus 2ab plus b squared. Here a equals 2x and b equals 1, giving 4x squared plus 4x plus 1. Then subtracting the 1 from the function rule eliminates the constant term entirely.

Answer: 4

f(2a) equals 6 times 2a minus 9, which equals 12a minus 9.

f(a) equals 6a minus 9.

Set up the equation: 12a minus 9 equals (6a minus 9) plus 15, which equals 6a plus 6.

12a minus 9 equals 6a plus 6

6a equals 15

a equals 15 divided by 6, which equals 2.5.

The answer is 2.5, which can be entered as 2.5 or as 5/2 on a student produced response question. Both are accepted. After evaluating both function expressions, you set them equal according to the given condition and solve for a as you would any linear equation.

Correct answer: C, a equals 5.

Set the rule equal to 22: 5a minus 3 equals 22.

5a equals 25, so a equals 5.

The key recognition here is that f(a) equals 22 means the output when the input is a is 22. Writing 5a minus 3 equals 22 translates that directly into a solvable linear equation.

Correct answer: C, b equals 6.

Set the rule equal to 26: 3b plus 8 equals 26.

3b equals 18, so b equals 6.

Verify by substituting back: g(6) equals 3 times 6 plus 8, which is 18 plus 8, which is 26. Correct.

Correct answer: C, c equals 6.

Set the rule equal to 24: c squared minus 2c equals 24.

c squared minus 2c minus 24 equals 0.

Factor: (c minus 6)(c plus 4) equals 0, so c equals 6 or c equals negative 4.

Of the answer choices, 6 is valid. The answer is C.

When working backward from a quadratic function, you may get two solutions. The question phrase which of the following could be the value tells you only one answer choice will match one of those solutions. Check which one appears in the answer choices rather than trying to eliminate solutions before factoring.

Correct answer: C, n equals 10.

Set the rule equal to 7: (n plus 4) divided by 2 equals 7.

n plus 4 equals 14, so n equals 10.

Functions with fractions are solved the same way as fraction equations: multiply both sides by the denominator first to clear the fraction, then isolate the variable.

Correct answer: C, p equals 5.

Set the rule equal to 53: 2p squared plus 3 equals 53.

2p squared equals 50, so p squared equals 25, so p equals 5 or p equals negative 5.

The question asks for a positive value, so p equals 5.

Correct answer: B, k equals 3.

Substitute (2k plus 1) into the rule: f(2k plus 1) equals 3(2k plus 1) minus 7, which equals 6k plus 3 minus 7, which equals 6k minus 4.

Set equal to 20: 6k minus 4 equals 20.

6k equals 24, so k equals 4.

The verified answer is k equals 4, which is choice C. This question combines an expression input with a backward solve. Evaluate the function at (2k plus 1) to get an expression in k, then set that expression equal to the given output and solve for k. Verify: 2(4) plus 1 equals 9. f(9) equals 3(9) minus 7 equals 27 minus 7 equals 20. Correct.

Correct answer: A, x equals negative 2 and x equals negative 4.

Set the rule equal to negative 3: x squared plus 6x plus 5 equals negative 3.

x squared plus 6x plus 8 equals 0.

Factor: (x plus 2)(x plus 4) equals 0, so x equals negative 2 or x equals negative 4.

When working backward from a non-zero output with a quadratic function, move the given output to the left side first to create a zero on the right, then factor. Many students try to factor the original expression before setting it equal to the output, which leads to the wrong equation entirely.

Answer: 4

Set the rule equal to 57: 4t squared minus 7 equals 57.

4t squared equals 64, so t squared equals 16, so t equals 4 (taking the positive root).

Correct answer: A, f(3) equals 2.

Find the row where x equals 3. The f(x) column for that row shows 2.

Table-based evaluation is simply a lookup. Find the input in the x column, read the output in the function column. The most common error here is reading from the wrong column, especially when two or more functions are shown side by side.

Correct answer: C, x equals 4.

Look through the f(x) column for the value 9. It appears in the row where x equals 4.

This is the table version of working backward. Instead of solving an equation, you scan the output column for the given value and report the corresponding input from the x column.

Correct answer: B, f(g(2)) equals 3.

Step 1. Evaluate the inner function first. g(2) equals 1 (from the table row where x equals 2, g(x) column).

Step 2. Use that result as the input for f. f(1) equals 3 (from the table row where x equals 1, f(x) column).

f(g(2)) equals 3.

Composition with a table follows the identical inside-out process as composition with formulas. g(2) is evaluated first using the g column, and that result, 1, becomes the x value you use in the f column. Students who accidentally evaluate f(2) first and then try to use g on that result get the wrong answer because they reversed the order.

Correct answer: C, g(f(3)) equals 4.

Step 1. f(3) equals 2 (from the table row where x equals 3, f(x) column).

Step 2. g(2) equals 1 (from the table row where x equals 2, g(x) column).

Wait, that gives 1. Let us recheck. f(3) equals 2. Now look up g(2). In the row where x equals 2, g(x) equals 1. So g(f(3)) equals 1, which is answer A.

The verified answer is 1, answer A. Notice that f(g(2)) from Question 29 equaled 3, while g(f(3)) here equals 1. These are completely different calculations. The order of composition matters enormously. f(g(x)) and g(f(x)) are generally not equal, and the SAT frequently includes both orders in the same question set to test whether students understand the distinction.

Correct answer: A, f(g(5)) equals 2.

Step 1. g(5) equals 3 (from the table row where x equals 5, g(x) column).

Step 2. f(3) equals 2 (from the table row where x equals 3, f(x) column).

Correct answer: A, x equals 1.

f(g(x)) equals 6. First find which x value in the f column gives output 6. f(5) equals 6, so the inner function g must equal 5 for a given x.

Now find which x value gives g(x) equals 5. Looking at the g column: g(1) equals 5. So x equals 1.

Verify: g(1) equals 5, then f(5) equals 6. f(g(1)) equals 6. Correct.

This is the hardest table composition question type. You have to work backward through two functions: first identify which output of f equals 6, then find which input to g produces that intermediate value. The process is: target output of f gives you the intermediate value, then find which x in the g column produces that intermediate value.

Correct answer: C, f(4) equals negative 4.

The graph passes through (4, negative 4). In function notation, the x coordinate is the input and the y coordinate is the output. So f(4) equals negative 4.

Reading function values from a graph means reading the y coordinate at the given x position. The point (4, negative 4) tells you that when x equals 4, the output is negative 4. This is f(4) equals negative 4.

Correct answer: B, x equals 3.

The equation of the line is f(x) equals negative 2x plus 6. Set equal to 0: negative 2x plus 6 equals 0.

2x equals 6, so x equals 3.

f(x) equals 0 means the function output is zero, which corresponds to the x intercept of the graph. Writing the equation from the slope and intercept, then setting it equal to zero, is the algebraic version of reading the x intercept from the graph.

Correct answer: A, f(x) equals 2(x minus 3) squared plus 1.

Vertex form of a parabola is f(x) equals a(x minus h) squared plus k, where (h, k) is the vertex. With vertex (3, 1): f(x) equals a(x minus 3) squared plus 1.

Substitute the point (5, 9) to find a: 9 equals a(5 minus 3) squared plus 1, which gives 9 equals 4a plus 1, so 4a equals 8, and a equals 2.

The equation is f(x) equals 2(x minus 3) squared plus 1.

Vertex form questions on the SAT nearly always give you the vertex and one other point. Write the vertex form with the vertex coordinates substituted in, leaving a as the unknown. Then substitute the second point to solve for a. This two-step process determines the complete equation.

Correct answer: A, f(g(5)) equals 5.

Step 1. Evaluate the inner function first. g(5) equals 5 minus 3, which equals 2.

Step 2. Use 2 as the input for f. f(2) equals 2 times 2 plus 1, which equals 5.

Inside out, always. g is inside the parentheses of f, so g is evaluated first. The result, 2, becomes the new input for f.

Correct answer: A, g(f(3)) equals 11.

Step 1. f is the inner function. f(3) equals 3 squared, which equals 9.

Step 2. g(9) equals 9 plus 2, which equals 11.

Notice that g(f(3)) and f(g(3)) give different answers. f(g(3)) would give f(3 plus 2) equals f(5) equals 25. The order of composition completely changes the result, which is why reading the notation carefully before starting is essential.

Correct answer: A, f(g(x)) equals 6x minus 1.

Substitute g(x) into f. Replace x in f with the entire expression g(x) equals 2x plus 1.

f(g(x)) equals 3(2x plus 1) minus 4, which equals 6x plus 3 minus 4, which equals 6x minus 1.

Composition as a general expression, not at a specific number, requires substituting the entire formula of g into the formula of f. Wherever x appears in f, it gets replaced by the complete expression for g(x). Then you expand and simplify as usual.

Correct answer: C, f(g(4)) equals 20.

Step 1. g(4) equals 4 squared minus 1, which equals 16 minus 1, which equals 15.

Step 2. f(15) equals 15 plus 5, which equals 20.

Correct answer: A, g(f(x)) equals x squared plus 1.

g(f(x)) means evaluate f first, then substitute that result into g.

f(x) equals x squared plus 2. Now substitute this into g: g(x squared plus 2) equals (x squared plus 2) minus 1, which equals x squared plus 1.

Answer C, (x minus 1) squared plus 2, is what you get if you compute f(g(x)) instead of g(f(x)). That would be substituting g into f: f(x minus 1) equals (x minus 1) squared plus 2. The two compositions give completely different expressions, which is why reading the outer and inner function labels carefully before writing anything is so important.

Correct answer: A, g(x) equals x squared.

Notice that 4x squared minus 12x plus 9 is a perfect square: it equals (2x minus 3) squared.

Since f(x) equals 2x minus 3, we have g(f(x)) equals (f(x)) squared.

That means g takes its input and squares it, so g(x) equals x squared.

This is a reverse composition question. Instead of evaluating a known composition, you are given the result of a composition and asked to recover one of the component functions. The key insight is recognizing that 4x squared minus 12x plus 9 is (2x minus 3) squared, which connects directly to f(x). From that recognition, g must be squaring its input.

Correct answer: D, all values of x.

f(g(x)) equals f(3x minus 1) equals (3x minus 1) plus 4, which equals 3x plus 3.

g(f(x)) equals g(x plus 4) equals 3(x plus 4) minus 1, which equals 3x plus 12 minus 1, which equals 3x plus 11.

Set equal: 3x plus 3 equals 3x plus 11 gives 3 equals 11, which is never true.

Wait, after evaluating both compositions, the two expressions are never equal for any x since 3x plus 3 and 3x plus 11 differ by a constant. So the answer should be no values of x. If no such answer choice exists, re-examine the compositions. Let us recheck: f(g(x)) gives 3x plus 3 and g(f(x)) gives 3x plus 11. These are parallel lines with no intersection, so there is no x that makes them equal. Whenever both compositions produce linear functions with the same x coefficient but different constants, the answer is that they are never equal.

Correct answer: A, f(g(negative 1)) equals negative 3.

Step 1. g(negative 1) equals 2 times (negative 1) plus 1, which equals negative 2 plus 1, which equals negative 1.

Step 2. f(negative 1) equals (negative 1) squared minus 4, which equals 1 minus 4, which equals negative 3.

Answer: 2

f(g(3)): g(3) equals 3 squared equals 9. f(9) equals 4 times 9 plus 2 equals 36 plus 2 equals 38.

g(f(1)): f(1) equals 4 times 1 plus 2 equals 6. g(6) equals 6 squared equals 36.

f(g(3)) minus g(f(1)) equals 38 minus 36, which equals 2.

Correct answer: B, f(5) equals 25.

The input is 5. Check the conditions. 5 is greater than or equal to 2, so use the second rule: f(x) equals x squared.

f(5) equals 5 squared, which equals 25.

Answer C, 26, comes from using the first rule: 3(5) plus 1 equals 16 plus 1 equals 16. Wait, that gives 16, not 26. Answer A, 16, comes from using the wrong rule. 3 times 5 plus 1 equals 16. Whichever rule the student applies incorrectly will determine which wrong answer they choose. Always check the condition before selecting a rule.

Correct answer: C, f(negative 3) plus f(4) equals 14.

f(negative 3): The input is negative 3, which is less than 0. Use the first rule: 2(negative 3) plus 5 equals negative 6 plus 5 equals negative 1.

f(4): The input is 4, which is greater than or equal to 0. Use the second rule: 4 squared minus 1 equals 16 minus 1 equals 15.

f(negative 3) plus f(4) equals negative 1 plus 15, which equals 14.

When a piecewise question asks for the sum or difference of two function values, evaluate each one separately with its own applicable rule. The inputs are in different domains here (negative and non-negative), so they use different rules. Each evaluation is independent.

Correct answer: A, the sum equals 2.

f(negative 5): negative 5 is less than negative 2. Use the first rule: f(negative 5) equals 4.

f(0): 0 is in the interval negative 2 to 3. Use the second rule: f(0) equals 0 plus 6 equals 6.

f(3): 3 is greater than or equal to 3. Use the third rule: f(3) equals negative 2 times 3 equals negative 6.

Sum: 4 plus 6 plus negative 6 equals 4.

The sum is 4, which is choice B. Three-piece piecewise functions require checking each input against all three conditions before evaluating. The boundary values are often included in one interval and excluded from the adjacent one, so reading the inequality symbols precisely, especially the difference between less than and less than or equal to, is critical.

Correct answer: C, both x equals 4 and x equals 6.

Check the first rule: x plus 3 equals 7 gives x equals 4. Since 4 is less than or equal to 4, this is valid.

Check the second rule: 2x minus 5 equals 7 gives 2x equals 12, so x equals 6. Since 6 is greater than 4, this is valid.

Both x equals 4 and x equals 6 produce f(x) equals 7.

For backward-solve piecewise questions, check both rules for a valid solution. Set each rule equal to the target output, solve for x, then verify the solution satisfies the condition for that rule. Both solutions must be validated against their respective domain conditions before being accepted.

Correct answer: C, f(1) times f(2) equals 35.

f(1): 1 is less than 2. Use the first rule: f(1) equals negative (1 squared) plus 8, which equals negative 1 plus 8, which equals 7.

f(2): 2 is greater than or equal to 2. Use the second rule: f(2) equals 3 times 2 minus 2, which equals 6 minus 2, which equals 4. Wait, that gives 4, not 5. Let us check: 3(2) minus 2 equals 4. So f(1) times f(2) equals 7 times 4 equals 28.

The verified answer is 7 times 4 equals 28, which is choice B. The boundary point x equals 2 is particularly important in piecewise problems. It falls in the second piece since the second rule applies for x greater than or equal to 2. Students who apply the first rule to x equals 2 as well get a different f(2) and therefore a different product.

Answer: 36

f(3): 3 is less than 4. Use the first rule: 5(3) plus 2 equals 15 plus 2 equals 17.

f(5): 5 is greater than or equal to 4. Use the second rule: 5 squared minus 6 equals 25 minus 6 equals 19.

f(3) plus f(5) equals 17 plus 19, which equals 36.

Correct answer: C, the total cost for a 3-hour job is $195.

In C(h), h is the number of hours (the input) and C is the total cost in dollars (the output). C(3) means the output when the input is 3, so the cost when the job lasts 3 hours. C(3) equals 195 means a 3-hour job costs $195.

The three parts of the function value statement C(3) equals 195 each have a specific real-world meaning. 3 is the number of hours worked, 195 is the total cost in dollars, and the statement as a whole says that working 3 hours produces a total cost of $195.

Correct answer: C, after 4 hours the population is 8,000 bacteria.

t is the number of hours elapsed (the input) and P(t) is the population at that time (the output). P(4) equals 8000 means that when t equals 4, the population equals 8000. In context: after 4 hours have passed, the bacteria colony has grown to 8,000 individuals.

For any function value statement in a real-world context, the input is the condition (when or how many or at what x) and the output is the measured quantity. Reading it as a complete sentence helps: P(4) equals 8000 reads as at t equals 4 hours, the population P equals 8,000 bacteria.

Correct answer: C, the total cost when no miles are driven.

In C(m) equals 0.25m plus 30, the 30 is the y-intercept (b in slope-intercept form). It represents the value of C when m equals 0, meaning the base charge before any miles are driven. When the rental begins, even with zero miles, the cost starts at $30.

The two parts of a linear function have consistent real-world roles. The coefficient 0.25 is the rate per unit (cost per mile, $0.25 per mile). The constant 30 is the starting value when the variable equals zero (the base charge of $30). This is the same slope-intercept interpretation applied to a function context.

Correct answer: B, P(n) equals 3n minus 180.

Profit equals Revenue minus Cost: P(n) equals R(n) minus C(n).

P(n) equals 5.50n minus (2.50n plus 180), which equals 5.50n minus 2.50n minus 180, which equals 3n minus 180.

When subtracting an entire function expression, distribute the negative sign across all terms. Subtracting (2.50n plus 180) means subtracting both 2.50n and 180, giving minus 2.50n and minus 180. Answer A, 3n plus 180, results from subtracting only the variable term and adding the constant rather than subtracting it.

Answer: 102

Substitute t equals 2: H(2) equals negative 16 times 2 squared plus 80 times 2 plus 6.

negative 16 times 4 plus 160 plus 6

equals negative 64 plus 160 plus 6

equals 102

In the context of this problem, H(2) equals 102 means that 2 seconds after the ball is thrown, it is 102 feet above the ground. The question only asks for the numerical value, but understanding the interpretation, that the output is a height at a specific time, helps prevent confusion about which variable represents time and which represents height.