Loading Lesson Content...

Back to Lesson: Function Transformations

Function Transformations

This worksheet covers Function Transformations, which is part of the Graphing and Transforming Functions module in the SAT Math course. Practice problems are designed to strengthen key concepts and build confidence.

More in Graphing and Transforming Functions

*View full SAT Math course with step by step lessons and online quiz modules.*

Want to reach top 5% in SAT Math?

Learn shortcut methods and time-saving strategies with our SAT Math Destroyer Crash Course.

View Destroyer Course →

Function Transformations

Graphing and Transforming Functions • SAT Math

Set 5 — Mastery

What is the equation of the function obtained by translating the function $f(x) = x^{2}$ 3 units to the right and 2 units up?

$f(x) = (x - 3)^{2} + 2$

$f(x) = (x + 3)^{2} + 2$

$f(x) = (x - 3)^{2} - 2$

$f(x) = (x + 3)^{2} - 2$

If $g(x) = -2x + 5$ , what is the effect of the negative sign on the graph of the function?

The graph is reflected over the x-axis.

The graph is reflected over the y-axis.

The graph is shifted up 2 units.

The graph is shifted down 2 units.

Which of the following transformations represents the function $h(x) = (x + 4)^{2} - 7$ ?

Shift left 4 units and down 7 units.

Shift right 4 units and up 7 units.

Shift left 4 units and up 7 units.

Shift right 4 units and down 7 units.

For the function $k(x) = 3|x - 1| + 2$ , what is the transformation applied to the basic absolute value function $|x|$ ?

Vertical stretch by a factor of 3, right shift by 1 unit, and up shift by 2 units.

Vertical compression by a factor of 3, left shift by 1 unit, and down shift by 2 units.

Vertical stretch by a factor of 3, left shift by 1 unit, and down shift by 2 units.

Vertical compression by a factor of 3, right shift by 1 unit, and up shift by 2 units.

What is the result of reflecting the graph of the function $f(x) = x^{3}$ over the y-axis?

$f(x) = -x^{3}$

$f(x) = x^{3} + 1$

$f(x) = x^{-3}$

$f(x) = -x^{2}$

If $f(x) = 2(x - 3)^{2} - 1$ , what is the vertex of the parabola represented by this function?

(3, -1)

(3, 1)

(-3, -1)

(-3, 1)

Which transformation does $f(x) = -|x + 2| + 5$ represent?

Shift left 2 units, reflect over the x-axis, and shift up 5 units.

Shift right 2 units, reflect over the y-axis, and shift down 5 units.

Shift left 2 units, reflect over the y-axis, and shift up 5 units.

Shift right 2 units, reflect over the x-axis, and shift up 5 units.

If $f(x) = (x + 1)^{2}$ is transformed to $g(x) = (x + 1)^{2} - 4$ , what transformation has occurred?

Shift down 4 units.

Shift up 4 units.

Shift left 4 units.

Shift right 4 units.

What is the effect of multiplying the function $f(x) = x^{2}$ by -1?

The graph is reflected over the x-axis.

The graph is reflected over the y-axis.

The graph is shifted down.

The graph is shifted up.

10.

Which of the following correctly describes the transformation of the function $f(x) = -3x^{2}$ ?

Vertical stretch by a factor of 3 and reflection over the x-axis.

Vertical compression by a factor of 3 and reflection over the y-axis.

Vertical stretch by a factor of 3 and shift down 3 units.

Vertical compression by a factor of 3 and shift up 3 units.

Feel free to use these worksheets in your classroom or share the link with students and colleagues!

Other Sets

Show answer choices

Set 1Foundation Set 2Foundation Set 3Foundation Set 4Mastery Set 5Mastery Custom Worksheet

Other Sets

Show answer choices

Set 1Foundation Set 2Foundation Set 3Foundation Set 4Mastery Set 5Mastery Custom Worksheet

Other Sets

Show answer choices

Set 1Foundation Set 2Foundation Set 3Foundation Set 4Mastery Set 5Mastery Custom Worksheet

Other Sets

Show answer choices

Set 1Foundation Set 2Foundation Set 3Foundation Set 4Mastery Set 5Mastery Custom Worksheet