Question 1

Which transformation is represented by the equation $$f(x) \rightarrow f(x-3)$$?

Accepted Answer

A horizontal shift right by 3 units

Question 2

Given $$f(x) = x^2$, what is the equation for the function reflected over the y$-axis and shifted up 2 units?

Accepted Answer

$$f(x) = (-x)^2$ + 2$$

Question 3

If $$g(x) is a $$reflection of $$f(x)$$ about the $$x-$$axis, which equation represents $$g(x)$$?

Accepted Answer

$$g(x) = -f(x)$$

Question 4

A function $$f(x) is $$vertically stretched by a factor of 4. Which equation represents this transformation?

Accepted Answer

$$f(x) = 4f(x)$$

Question 5

Given $$f(x) = x^2$, what is the equation for the function that is reflected over the x$-axis and shifted down 2 units?

Accepted Answer

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

Question 6

Which transformation will change the domain of $$f(x)$$ from $$[-1, 3] to$$ $$[1, 5]$$?

Accepted Answer

A horizontal shift right by 2 units

Question 7

If $$f(x) is $$compressed horizontally by a factor of $$\frac{1}{2}$$, what is the new equation?

Accepted Answer

$$f(x) = f(2x)$$

Question 8

Given $$f(x) = x^2$, what is the equation for the function shifted left by 4 units and down by 1 unit?

Accepted Answer

$$f(x) = (x+4)^2$ - 1$$

Question 9

Which transformation is represented by $$f(x) \rightarrow f(x) - 5$$?

Accepted Answer

Vertical shift down by 5 units

Question 10

If $$f(x) is $$reflected over the $$y-$$axis and then shifted right by 2 units, what is the equation for the new function?

Accepted Answer

$$f(x) = f(-(x-2))$$

Question 11

Given $$f(x)$$, which transformation will result in a graph that is both reflected over the $$x-$$axis and vertically stretched by a factor of 3?

Accepted Answer

$$g(x) = -3f(x)$$

Question 12

If $$f(x)$$ has a range of $$[2, 8]$$, what is the range of $$g(x) = f(x) + 4$$?

Accepted Answer

$$[6, 12]$$

Question 13

Which transformation is represented by $$f(x) \rightarrow f(-x)$$?

Accepted Answer

Reflection over the $$y-$$axis

Question 14

Given $$f(x) = x^2$, what is the equation for the function that is horizontally stretched by a factor of 2?

Accepted Answer

$$f(x) = (\frac{x}{2})^2$

Question 15

If $$f(x) is $$shifted up by 7 units and left by 3 units, what is the equation for the new function?

Accepted Answer

$$g(x) = f(x+3) + 7$$

Question 16

Which transformation will shrink the graph of $$f(x)$$ vertically by a factor of $$\frac{1}{3}$$?

Accepted Answer

$$f(x) = \frac{1}{3}f(x)$$

Question 17

Given $$f(x)$$, what is the equation for the function that is reflected over the $$x-$$axis and shifted left by 5 units?

Accepted Answer

$$g(x) = -f(x+5)$$

Question 18

If $$f(x) is $$compressed horizontally by a factor of $$\frac{1}{4}$$ and shifted up by 2 units, what is the equation for the new function?

Accepted Answer

$$g(x) = f(4x) + 2$$

Question 19

Given $$f(x)$$, which transformation will result in a graph that is reflected over the $$y-$$axis and shifted down by 6 units?

Accepted Answer

$$g(x) = f(-x) - 6$$

Study Guide: Transformations of Functions in Precalculus

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