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SAT function transformations practice questions test whether students can recognize vertical and horizontal shifts, reflections, stretches, and compressions from function notation, and connect these transformations to graphs, points, and real-world models. This guide includes 70 SAT-style questions covering transformation basics, effects on specific points, parameter questions, graphs and word problems, and student-produced responses.
What Should You Know Before Practicing Function Transformation Questions?
In This Guide – 70 SAT Function Transformations Practice Questions
Start With SAT Math Topic-Wise Practice
Practice becomes more useful when it is connected to a weekly score plan, mock test review, and targeted SAT Math correction.
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Use the SAT Prep Guide E-Book to review function transformations, plan weekly SAT Math practice, and connect every practice set with a clear score improvement strategy.
Download SAT Prep Guide E-BookFunction transformation questions belong to SAT Advanced Math and SAT Algebra because they connect abstract function notation to graphs. Students may be asked to identify a transformation from an equation, find a corresponding point after a transformation, find a parameter value that produces a specific shift or stretch, or interpret a transformation in a real-world model.
The best SAT strategy is to isolate each transformation one piece at a time — shift, reflect, then stretch or compress — rather than trying to visualize every change at once.
| Transformation | Effect on Graph | Direction | SAT Trap |
|---|---|---|---|
| f(x) + k | Vertical shift | Up if k > 0, down if k < 0 | Confusing it with a horizontal shift |
| f(x – h) | Horizontal shift | Right if h > 0, left if h < 0 | Reversing the direction of the shift |
| -f(x) or f(-x) | Reflection | Over x-axis or y-axis, respectively | Mixing up which axis is used |
SAT strategy: Before answering, identify whether the change is inside or outside the function notation. Changes outside (adding/multiplying after f(x)) affect y-values; changes inside (adding/multiplying x before applying f) affect x-values and often work in the opposite direction you’d expect.
To begin your preparation with organized practice, download our free SAT Prep E-Book, SAT Math Question Bank, and SAT English Question Bank. These tools are intended to assist students in comprehending the style of the Digital SAT, increasing their accuracy, and boosting their self-assurance prior to test day.
Start with the basic transformation rules. On the SAT, you often do not need to graph anything. You only need to classify the transformation directly from the equation.
The function g(x) = f(x) + 4 is obtained from f(x) by which transformation?
Which choice is correct?
A) Shift up 4
B) Shift down 4
C) Shift left 4
D) Shift right 4
Adding a constant outside f(x) shifts the graph vertically up by that amount. Answer: A
The function g(x) = f(x) – 6 is obtained from f(x) by which transformation?
Which choice is correct?
A) Shift up 6
B) Shift down 6
C) Shift left 6
D) Shift right 6
Subtracting a constant outside f(x) shifts the graph down by that amount. Answer: B
The function g(x) = f(x – 5) is obtained from f(x) by which transformation?
Which choice is correct?
A) Shift left 5
B) Shift right 5
C) Shift up 5
D) Shift down 5
Subtracting inside the parentheses shifts the graph right by that amount. Answer: B
The function g(x) = f(x + 3) is obtained from f(x) by which transformation?
Which choice is correct?
A) Shift left 3
B) Shift right 3
C) Shift up 3
D) Shift down 3
Adding inside the parentheses shifts the graph left by that amount. Answer: A
The function g(x) = -f(x) is obtained from f(x) by which transformation?
Which choice is correct?
A) Reflection over the x-axis
B) Reflection over the y-axis
C) Vertical stretch
D) Horizontal stretch
Negating the output flips the graph over the x-axis. Answer: A
The function g(x) = f(-x) is obtained from f(x) by which transformation?
Which choice is correct?
A) Reflection over the x-axis
B) Reflection over the y-axis
C) Vertical stretch
D) Horizontal stretch
Negating the input flips the graph over the y-axis. Answer: B
The function g(x) = 3f(x) is obtained from f(x) by which transformation?
Which choice is correct?
A) Vertical stretch by a factor of 3
B) Vertical compression by a factor of 3
C) Horizontal stretch by a factor of 3
D) Horizontal compression by a factor of 3
Multiplying the output by a number greater than 1 stretches the graph vertically. Answer: A
The function g(x) = (1/2)f(x) is obtained from f(x) by which transformation?
Which choice is correct?
A) Vertical stretch by a factor of 2
B) Vertical compression by a factor of 1/2
C) Horizontal stretch by a factor of 2
D) Horizontal compression by a factor of 1/2
Multiplying the output by a number between 0 and 1 compresses the graph vertically. Answer: B
The function g(x) = f(2x) is obtained from f(x) by which transformation?
Which choice is correct?
A) Horizontal compression by a factor of 1/2
B) Horizontal stretch by a factor of 2
C) Vertical compression by a factor of 1/2
D) Vertical stretch by a factor of 2
Multiplying the input by a number greater than 1 compresses the graph horizontally. Answer: A
The function g(x) = f(x/3) is obtained from f(x) by which transformation?
Which choice is correct?
A) Horizontal stretch by a factor of 3
B) Horizontal compression by a factor of 3
C) Vertical stretch by a factor of 3
D) Vertical compression by a factor of 3
Dividing the input stretches the graph horizontally by that factor. Answer: A
The function g(x) = f(x + 7) – 2 is obtained from f(x) by which transformation?
Which choice is correct?
A) Shift left 7 and down 2
B) Shift right 7 and up 2
C) Shift left 7 and up 2
D) Shift right 7 and down 2
The +7 inside the parentheses shifts left 7, and the -2 outside shifts down 2. Answer: A
The function g(x) = f(x – 4) + 5 is obtained from f(x) by which transformation?
Which choice is correct?
A) Shift right 4 and up 5
B) Shift left 4 and down 5
C) Shift right 4 and down 5
D) Shift left 4 and up 5
The -4 inside the parentheses shifts right 4, and the +5 outside shifts up 5. Answer: A
The function g(x) = -f(x) + 6 is obtained from f(x) by which transformation?
Which choice is correct?
A) Reflect over the x-axis, then shift up 6
B) Reflect over the y-axis, then shift up 6
C) Reflect over the x-axis, then shift down 6
D) Reflect over the y-axis, then shift down 6
The negative sign in front reflects over the x-axis, and the +6 shifts the result up 6. Answer: A
The function g(x) = f(-x) – 3 is obtained from f(x) by which transformation?
Which choice is correct?
A) Reflect over the x-axis, then shift down 3
B) Reflect over the y-axis, then shift down 3
C) Reflect over the x-axis, then shift up 3
D) Reflect over the y-axis, then shift up 3
The -x inside f reflects over the y-axis, and the -3 outside shifts the result down 3. Answer: B
The function g(x) = 2f(x – 1) is obtained from f(x) by which transformation?
Which choice is correct?
A) Shift right 1, vertical stretch by 2
B) Shift left 1, vertical stretch by 2
C) Shift right 1, vertical compression by 2
D) Shift left 1, vertical compression by 2
The -1 inside shifts right 1, and the 2 outside stretches the result vertically by a factor of 2. Answer: A
The function g(x) = f(x) + 8 is obtained from f(x) by which transformation?
Which choice is correct?
A) Shift up 8
B) Shift down 8
C) Shift left 8
D) Shift right 8
Adding a constant outside f(x) shifts the graph vertically up by that amount. Answer: A
The function g(x) = f(x + 9) is obtained from f(x) by which transformation?
Which choice is correct?
A) Shift left 9
B) Shift right 9
C) Shift up 9
D) Shift down 9
Adding inside the parentheses shifts the graph left by that amount. Answer: A
The function g(x) = -2f(x) is obtained from f(x) by which transformation?
Which choice is correct?
A) Reflect over the x-axis and stretch vertically by 2
B) Reflect over the y-axis and stretch vertically by 2
C) Reflect over the x-axis and compress vertically by 2
D) Reflect over the y-axis and compress vertically by 2
The negative sign reflects over the x-axis, and the factor of 2 stretches the graph vertically. Answer: A
The function g(x) = f(3x) is obtained from f(x) by which transformation?
Which choice is correct?
A) Horizontal compression by a factor of 1/3
B) Horizontal stretch by a factor of 3
C) Vertical compression by a factor of 1/3
D) Vertical stretch by a factor of 3
Multiplying the input by a number greater than 1 compresses the graph horizontally. Answer: A
The function g(x) = f(x) – 10 is obtained from f(x) by which transformation?
Which choice is correct?
A) Shift up 10
B) Shift down 10
C) Shift left 10
D) Shift right 10
Subtracting a constant outside f(x) shifts the graph down by that amount. Answer: B
The function g(x) = f(x – 8) is obtained from f(x) by which transformation?
Which choice is correct?
A) Shift left 8
B) Shift right 8
C) Shift up 8
D) Shift down 8
Subtracting inside the parentheses shifts the graph right by that amount. Answer: B
The function g(x) = (1/4)f(x) is obtained from f(x) by which transformation?
Which choice is correct?
A) Vertical stretch by a factor of 4
B) Vertical compression by a factor of 1/4
C) Horizontal stretch by a factor of 4
D) Horizontal compression by a factor of 1/4
Multiplying the output by a number between 0 and 1 compresses the graph vertically. Answer: B
The function g(x) = f(x/2) is obtained from f(x) by which transformation?
Which choice is correct?
A) Horizontal stretch by a factor of 2
B) Horizontal compression by a factor of 2
C) Vertical stretch by a factor of 2
D) Vertical compression by a factor of 2
Dividing the input stretches the graph horizontally by that factor. Answer: A
The function g(x) = -f(-x) is obtained from f(x) by which transformation?
Which choice is correct?
A) Reflection over both axes (equivalent to a 180° rotation)
B) Reflection over the x-axis only
C) Reflection over the y-axis only
D) No reflection occurs
Negating both the input and the output reflects the graph over both axes, equivalent to a 180° rotation about the origin. Answer: A
The function g(x) = f(x + 2) + 3 is obtained from f(x) by which transformation?
Which choice is correct?
A) Shift left 2, up 3
B) Shift right 2, down 3
C) Shift left 2, down 3
D) Shift right 2, up 3
The +2 inside shifts left 2, and the +3 outside shifts up 3. Answer: A
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Build accuracy by practicing function transformations, parabolas, discriminant, functions, and SAT Algebra in separate topic-wise sets.
These questions connect a known point on f(x) to the corresponding point on a transformed function g(x). This is where students save time by tracking the point instead of the whole graph.
If f(3) = 7 and g(x) = f(x) + 5, what is g(3)?
Which choice is correct?
A) 12
B) 7
C) 2
D) 15
g(3) = f(3) + 5 = 7 + 5 = 12. Answer: A
If f(4) = 9 and g(x) = f(x – 2), which point must be on the graph of g?
Which choice is correct?
A) (6, 9)
B) (2, 9)
C) (4, 11)
D) (4, 7)
g(6) = f(6 – 2) = f(4) = 9, so the point (6, 9) is on g. Answer: A
If f(-1) = 5 and g(x) = -f(x), what is g(-1)?
Which choice is correct?
A) 5
B) -5
C) 1
D) -1
g(-1) = -f(-1) = -5. Answer: B
If f(2) = 6 and g(x) = f(-x), which point must be on the graph of g?
Which choice is correct?
A) (-2, 6)
B) (2, -6)
C) (2, 6)
D) (-2, -6)
g(-2) = f(-(-2)) = f(2) = 6, so the point (-2, 6) is on g. Answer: A
If f(5) = 3 and g(x) = 2f(x), what is g(5)?
Which choice is correct?
A) 6
B) 3
C) 1.5
D) 10
g(5) = 2f(5) = 2(3) = 6. Answer: A
If (4, 10) is on the graph of f, and g(x) = f(x) – 4, which point is on the graph of g?
Which choice is correct?
A) (4, 6)
B) (4, 14)
C) (0, 10)
D) (8, 10)
g(4) = f(4) – 4 = 10 – 4 = 6, so the point (4, 6) is on g. Answer: A
If (6, 2) is on the graph of f, and g(x) = f(x + 3), which point is on the graph of g?
Which choice is correct?
A) (3, 2)
B) (9, 2)
C) (6, 5)
D) (6, -1)
g(3) = f(3 + 3) = f(6) = 2, so the point (3, 2) is on g. Answer: A
If (0, 4) is on the graph of f, and g(x) = f(x) + 7, which point is on the graph of g?
Which choice is correct?
A) (0, 11)
B) (7, 4)
C) (0, -3)
D) (-7, 4)
g(0) = f(0) + 7 = 4 + 7 = 11, so the point (0, 11) is on g. Answer: A
If (-3, 8) is on the graph of f, and g(x) = -f(x), which point is on the graph of g?
Which choice is correct?
A) (-3, -8)
B) (3, 8)
C) (-3, 8)
D) (3, -8)
g(-3) = -f(-3) = -8, so the point (-3, -8) is on g. Answer: A
If (5, -2) is on the graph of f, and g(x) = f(x – 5), which point is on the graph of g?
Which choice is correct?
A) (10, -2)
B) (0, -2)
C) (5, 3)
D) (5, -7)
g(10) = f(10 – 5) = f(5) = -2, so the point (10, -2) is on g. Answer: A
Parameter questions ask for a value of k, h, a, or b that produces a specific shift, reflection, stretch, or compression. Translate the description into an equation involving the parameter first.
For g(x) = f(x) + k, what value of k makes g a shift up 9?
Which choice is correct?
A) 9
B) -9
C) 1/9
D) 0
A vertical shift up by k requires k = 9. Answer: A
For g(x) = f(x – h), what value of h makes g a shift right 6?
Which choice is correct?
A) 6
B) -6
C) 1/6
D) 0
A shift right by h requires h = 6. Answer: A
For g(x) = f(x + h), what value of h makes g a shift left 4?
Which choice is correct?
A) 4
B) -4
C) 1/4
D) 0
Since f(x + h) shifts left by h, h must equal 4. Answer: A
For g(x) = a f(x), what value of a makes the graph a vertical stretch by a factor of 5?
Which choice is correct?
A) 5
B) 1/5
C) -5
D) 0
A vertical stretch by a factor of 5 requires a = 5. Answer: A
For g(x) = a f(x), what value of a makes the graph a vertical compression by a factor of 1/3?
Which choice is correct?
A) 3
B) 1/3
C) -3
D) -1/3
A vertical compression to 1/3 of the height requires a = 1/3. Answer: B
For g(x) = f(bx), what value of b makes the graph a horizontal compression by a factor of 1/4?
Which choice is correct?
A) 4
B) 1/4
C) -4
D) -1/4
A horizontal compression to 1/4 of the width requires b = 4. Answer: A
For g(x) = f(bx), what value of b makes the graph a horizontal stretch by a factor of 5?
Which choice is correct?
A) 5
B) 1/5
C) -5
D) -1/5
A horizontal stretch by a factor of 5 requires b = 1/5. Answer: B
If g(x) = f(x – h) + k represents a shift right 3 and up 8, what are h and k?
Which choice is correct?
A) h = 3, k = 8
B) h = -3, k = 8
C) h = 3, k = -8
D) h = -3, k = -8
A shift right 3 requires h = 3, and a shift up 8 requires k = 8. Answer: A
If g(x) = f(x + h) – k represents a shift left 5 and down 2, what are h and k?
Which choice is correct?
A) h = 5, k = 2
B) h = -5, k = 2
C) h = 5, k = -2
D) h = -5, k = -2
A shift left 5 requires h = 5, and a shift down 2 requires k = 2. Answer: A
For g(x) = a f(x – 2), if g(4) = 3f(2), what is the value of a?
Which choice is correct?
A) 2
B) 3
C) 4
D) 6
g(4) = a f(4 – 2) = a f(2). Setting this equal to 3f(2) gives a = 3. Answer: B
For g(x) = f(x) + k, if f(3) = 5 and g(3) = 12, what is the value of k?
Which choice is correct?
A) 5
B) 7
C) 12
D) 17
12 = 5 + k, so k = 7. Answer: B
For g(x) = f(x – h), if f(2) = 9 and g(6) = 9, what is the value of h?
Which choice is correct?
A) 2
B) 4
C) 6
D) 8
g(6) = f(6 – h) = 9 = f(2), so 6 – h = 2, giving h = 4. Answer: B
For g(x) = a f(x), if f(5) = 4 and g(5) = 20, what is the value of a?
Which choice is correct?
A) 4
B) 5
C) 16
D) 24
20 = a(4), so a = 5. Answer: B
For g(x) = f(bx), if f(8) = 6 and g(2) = 6, what is the value of b?
Which choice is correct?
A) 2
B) 4
C) 6
D) 16
g(2) = f(2b) = 6 = f(8), so 2b = 8, giving b = 4. Answer: B
For g(x) = -f(x) + k, if the maximum value of f is 5 and the minimum value of g is -1, what is the value of k?
Which choice is correct?
A) -4
B) 4
C) -6
D) 6
Reflecting f gives a minimum of -f’s maximum, which is -5. Then -5 + k = -1, so k = 4. Answer: B
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Build accuracy by practicing function transformations, parabolas, discriminant, functions, and SAT Algebra in separate topic-wise sets.
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Graph and word problems test the same skill in a more applied way. The transformation rule tells you how the graph moves, and the context tells you what that movement means.
The graph of f(x) is shifted 3 units right and 2 units down to create g(x). Which equation represents g(x)?
Which choice is correct?
A) g(x) = f(x – 3) – 2
B) g(x) = f(x + 3) + 2
C) g(x) = f(x – 3) + 2
D) g(x) = f(x + 3) – 2
Shifting right 3 requires subtracting 3 inside, and shifting down 2 requires subtracting 2 outside. Answer: A
The graph of f(x) is reflected over the x-axis and shifted up 5 to create g(x). Which equation represents g(x)?
Which choice is correct?
A) g(x) = -f(x) + 5
B) g(x) = f(-x) + 5
C) g(x) = -f(x) – 5
D) g(x) = f(-x) – 5
Reflecting over the x-axis negates the output, and shifting up 5 adds 5 afterward. Answer: A
The graph of y = f(x) has a maximum at (2, 9). What is the maximum point on y = f(x) + 4?
Which choice is correct?
A) (2, 13)
B) (6, 9)
C) (2, 5)
D) (-2, 9)
Adding 4 shifts the graph vertically, so the maximum becomes (2, 9 + 4) = (2, 13). Answer: A
The graph of y = f(x) has a minimum at (-3, -6). What is the minimum point on y = f(x – 5)?
Which choice is correct?
A) (2, -6)
B) (-8, -6)
C) (-3, -1)
D) (-3, -11)
Subtracting 5 inside shifts the graph right 5, so the minimum becomes (-3 + 5, -6) = (2, -6). Answer: A
A company’s cost function is C(x) = f(x) + 200, where f(x) is the base production cost. What does the 200 represent?
Which choice is correct?
A) A fixed cost added to production
B) A discount applied to production
C) A horizontal shift in units produced
D) A percentage increase
Adding 200 outside f(x) is a vertical shift, which represents a fixed cost added regardless of x. Answer: A
A temperature model is T(t) = f(t – 3), where f(t) models a typical day. What does the shift of 3 represent?
Which choice is correct?
A) The pattern is delayed by 3 hours
B) The pattern is 3 degrees warmer
C) The pattern repeats every 3 hours
D) The pattern is compressed by 3
Subtracting inside the function is a horizontal shift, meaning the same pattern happens 3 hours later. Answer: A
A graph shows y = f(x) reflected over the y-axis. Which equation represents this new graph?
Which choice is correct?
A) y = f(-x)
B) y = -f(x)
C) y = f(x) + 1
D) y = -f(-x)
Reflecting over the y-axis negates the input. Answer: A
Which transformation of f(x) results in a graph that is the mirror image of f(x) across both the x-axis and y-axis?
Which choice is correct?
A) g(x) = -f(-x)
B) g(x) = f(-x)
C) g(x) = -f(x)
D) g(x) = f(x)
Negating both the input and the output reflects the graph over both axes. Answer: A
A student says that f(x + 2) shifts the graph of f(x) to the right by 2. What is the best response?
Which choice is correct?
A) Incorrect; f(x + 2) shifts the graph left by 2
B) Correct
C) Incorrect; f(x + 2) shifts the graph up by 2
D) Incorrect; f(x + 2) reflects the graph
Adding inside the parentheses shifts the graph left, not right — a common sign-direction trap. Answer: A
The function f(x) = x² is transformed to g(x) = (x – 4)² + 1. What is the vertex of g(x)?
Which choice is correct?
A) (4, 1)
B) (-4, 1)
C) (4, -1)
D) (-4, -1)
The parent vertex (0, 0) shifts right 4 and up 1, landing at (4, 1). Answer: A
The graph of f(x) is vertically stretched by a factor of 3 and shifted down 2 to create g(x). Which equation represents g(x)?
Which choice is correct?
A) g(x) = 3f(x) – 2
B) g(x) = 3f(x) + 2
C) g(x) = f(3x) – 2
D) g(x) = f(3x) + 2
Multiplying f(x) by 3 stretches it vertically, and subtracting 2 afterward shifts it down. Answer: A
A sound wave model is transformed to g(x) = f(4x). Compared to f(x), how does g(x) behave?
Which choice is correct?
A) It completes each cycle in 1/4 the horizontal distance
B) It completes each cycle in 4 times the horizontal distance
C) It is 4 times as tall
D) It is 1/4 as tall
Multiplying the input by 4 compresses the graph horizontally, so cycles complete in 1/4 the horizontal distance. Answer: A
The graph of f(x) passes through (0, 0). After the transformation g(x) = f(x) – 6, which point is on g(x) corresponding to the origin?
Which choice is correct?
A) (0, -6)
B) (6, 0)
C) (0, 6)
D) (-6, 0)
g(0) = f(0) – 6 = 0 – 6 = -6, so the point (0, -6) is on g. Answer: A
Which single transformation turns f(x) = x² into g(x) = x² – 9?
Which choice is correct?
A) Vertical shift down 9
B) Vertical shift up 9
C) Horizontal shift right 9
D) Horizontal shift left 9
Subtracting 9 outside the squared term shifts the graph down 9. Answer: A
A student claims that g(x) = f(x – 3) and g(x) = f(x) – 3 produce the same graph. What is the best response?
Which choice is correct?
A) Incorrect; one shifts the graph horizontally and the other shifts it vertically
B) Correct; both shift the graph the same way
C) Incorrect; one reflects the graph
D) Correct; both shift the graph right by 3
f(x – 3) shifts the graph right by 3, while f(x) – 3 shifts it down by 3 — these are different transformations. Answer: A
These grid-in style questions require a number, not a multiple-choice selection. Read carefully whether the question asks for a function value, a coordinate, or a parameter.
Student-produced response: If f(2) = 7 and g(x) = f(x) + 5, what is g(2)?
g(2) = f(2) + 5 = 7 + 5 = 12. Answer: 12
Student-produced response: If (3, 8) is a point on f(x), and g(x) = f(x – 4), what is the x-coordinate of the corresponding point on g(x)?
We need x – 4 = 3, so x = 7. Answer: 7
Student-produced response: If f(6) = 10 and g(x) = a f(x) with g(6) = 40, what is the value of a?
40 = a(10), so a = 4. Answer: 4
Student-produced response: The graph of f(x) has vertex (5, -3). What is the y-coordinate of the vertex of g(x) = f(x) + 8?
-3 + 8 = 5. Answer: 5
Student-produced response: If g(x) = f(x + h) represents a shift left 7, what is the value of h?
Adding h inside the parentheses shifts the graph left by h, so h = 7. Answer: 7
| Mistake | Why It Hurts | Fix |
|---|---|---|
| Reversing the direction of a horizontal shift | f(x – h) shifts right, and f(x + h) shifts left — the opposite of what many students expect. | Rewrite f(x + h) as f(x – (-h)) to confirm the direction. |
| Confusing vertical and horizontal changes | Changes outside f(x) affect y-values; changes inside affect x-values. | Check whether the change is applied before or after f is evaluated. |
| Mixing up which axis a reflection uses | -f(x) reflects over the x-axis, while f(-x) reflects over the y-axis. | Remember: negating the output flips vertically, negating the input flips horizontally. |
| Assuming a stretch and compression work the same way inside and outside f | a·f(x) and f(bx) affect the graph in opposite ways for the same value. | A large a stretches vertically; a large b compresses horizontally. |
| Study Days | Focus | Practice Goal |
|---|---|---|
| Days 1–3 | Vertical and horizontal shifts | Do 20 quick shift-classification questions |
| Days 4–6 | Reflections and stretches/compressions | Connect the sign and size of each parameter to the graph change |
| Days 7–10 | Points and parameter questions | Practice tracking a single point through a transformation |
| Days 11–14 | Mixed timed SAT questions | Review every mistake and write the reason |
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|---|---|---|
| SAT Math Topic-Wise Practice Questions | Function transformations, parabolas, discriminant, algebra, and geometry practice | Browse Sets |
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They are changes to a function’s graph — shifts, reflections, stretches, and compressions — produced by adding, subtracting, or multiplying values inside or outside the function notation.
Yes, both as direct identification questions and inside graph or real-world modeling questions within SAT Algebra and Advanced Math.
Because the input to f must be h larger to produce the same output, so the graph’s key features occur at larger x-values, shifting the graph right.
-f(x) negates the output and reflects the graph over the x-axis, while f(-x) negates the input and reflects the graph over the y-axis.
Tracking a single known point through each transformation is usually faster than graphing the entire function on the SAT.
Yes, they span both SAT Algebra and SAT Advanced Math, since transformations apply to linear, quadratic, and other function types.
Reversing the direction of a horizontal shift, since f(x – h) and f(x + h) shift in the opposite direction from what many students first assume.
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