Question 1

Which of the following represents a reflection of the function $$f(x)$$ over the y-axis?

Accepted Answer

$$f(-x)$$

Question 2

Given $$f(x) = x^2$, which equation represents the graph of f(x$$)$$ shifted 3 units to the right and 2 units up?

Accepted Answer

$$f(x-3) + 2$$

Question 3

If $$g(x) is a $$reflection of $$f(x) = \sqrt{x-2}$$ about the y-axis, what is the equation for $$g(x)$$?

Accepted Answer

$$\sqrt{-x+2}$$

Question 4

A function $$f(x) is $$transformed to $$h(x) by $$reflecting over the x-axis and then shifting down 2 units. If $$f(x) = x^3$, what is h(x$$)$$?

Accepted Answer

$$-x^3 - 2$

Question 5

Which transformation will move the graph of $$f(x)$$ left by 4 units and up by 1 unit?

Accepted Answer

$$f(x+4) + 1$$

Question 6

Given $$f(x) = |x|$$, which equation represents a vertical stretch by a factor of 3?

Accepted Answer

$$3|x|$$

Question 7

If $$f(x) is $$reflected over the x-axis and then shifted 5 units up, which equation represents the transformation?

Accepted Answer

$$-f(x) + 5$$

Question 8

A function $$f(x) is $$shifted horizontally 2 units to the left and vertically 3 units down. What is the transformed function?

Accepted Answer

$$f(x+2) - 3$$

Question 9

Given $$f(x) = |x|$$, which transformation results in $$g(x) = -|x-1| + 2$$?

Accepted Answer

Reflect over x-axis, shift right 1 unit, shift up 2 units

Question 10

If $$f(x) is $$transformed to $$g(x) = f(-x) + 4$$, which sequence of transformations has occurred?

Accepted Answer

Reflection over y-axis, then shift up 4 units

Question 11

Which of the following is the result of reflecting $$f(x) = x^2$ over the y-axis and then shifting it 3 units to the left?

Accepted Answer

$$f(-x-3)$$

Question 12

A function $$f(x) is $$stretched vertically by a factor of $$c$$ and then shifted down $$k$$ units. Which equation represents this transformation?

Accepted Answer

$$c f(x) - k$$

Question 13

Given $$f(x) = |x|$$, which graph matches $$r(x) = -4|x|$$?

Accepted Answer

Reflected over x-axis and stretched vertically by 4

Question 14

If $$f(x) is $$shifted horizontally $$h$$ units and vertically $$k$$ units, what is the general form of the transformed function?

Accepted Answer

$$f(x-h) + k$$

Question 15

A function $$f(x) is $$reflected over the x-axis, shifted right 2 units, and up 3 units. What is the equation for the transformed function?

Accepted Answer

$$-f(x-2) + 3$$

Question 16

Which transformation would result in the graph of $$f(x)$$ being squeezed horizontally by a factor of $$c$$?

Accepted Answer

$$f(cx)$$

Question 17

Given $$f(x) = x^2$, what is the equation for the graph reflected over the x-axis and shifted left 5 units?

Accepted Answer

$$-f(x+5)$$

Question 18

If $$f(x) is $$shifted up 7 units and then reflected over the y-axis, what is the equation for the transformation?

Accepted Answer

$$f(-x) + 7$$

Question 19

A function $$f(x) is $$reflected over the y-axis and then shifted down 4 units. Which equation represents this transformation?

Accepted Answer

$$f(-x) - 4$$

Transformations of Functions: Reflections, Shifts, and Stretches

Study Guide - Practice Questions