$$[\text{minimum value}, \infty)$$

$$x \u003e 0$$ and $$x \neq -2$$

Question 1

What is the domain of the function $$f(x) = \sqrt{x-9}$$?

Accepted Answer

$$[9, \infty)$$

Question 2

Given $$g(x) = \dfrac{x}{x^2$ - 6}$$, which of the following describes its domain?

Accepted Answer

$$x 
eq \pm \sqrt{6}$$

Question 3

Which transformation is represented by $$y = f(x) + c$$ for $$c \u003e 0$$?

Accepted Answer

A vertical shift upward by $$c$$ units

Question 4

If $$f(x) is an $$even function, which symmetry does its graph have?

Accepted Answer

Symmetry about the $$y-$$axis

Question 5

Given $$f(x) = x^2$ and g(x) = x+1$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$(x+1)^2$$

Question 6

Which of the following describes the effect of the transformation $$y = f(-x)$$?

Accepted Answer

Reflection about the $$y-$$axis

Question 7

Suppose $$f(x) = \sqrt{x+1}$$ and $$g(x) = x^2$ - 16. $$What is the domain of $$f+g$$?

Accepted Answer

$$[-1, \infty)$$

Question 8

Given $$f(x) = 2x^2$ - 5x$$, what is the range of $$f(x)$$?

Accepted Answer

$$[	ext{minimum value}, \infty)$$

Question 9

Which of the following is the correct order of operations for multiple transformations on a function?

Accepted Answer

Horizontal shifts, then stretches/compressions, then reflections, then vertical shifts

Question 10

If $$f(x) = \sqrt{x}$$, what is the graph of $$y = -f(x)$$?

Accepted Answer

The graph of $$f(x)$$ reflected about the $$x-$$axis

Question 11

Given $$f(x) = \dfrac{12}{2x+4}$$ and $$g(x) = \sqrt{x}$$, what is the domain of $$f \cdot g$$?

Accepted Answer

$$x \u003e 0$$ and $$x 
eq -2$$

Question 12

Which transformation is represented by $$y = f(ax)$$ for $$a \u003e 1$$?

Accepted Answer

Horizontal compression by a factor of $$a$$

Question 13

If $$f(x) is $$odd, which of the following is true?

Accepted Answer

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

Question 14

Given $$f(x) = x^3$ - 3x^2$ + 2x$$, solve the inequality $$f(x) \geq 0.$$

Accepted Answer

$$x \leq 0 or$$ $$x = 1 or$$ $$x \geq 2$$

Question 15

Which of the following is the correct definition of a one-to-one function?

Accepted Answer

Each $$y in $$the range is paired with exactly one $$x in $$the domain

Question 16

Given $$f(x) = 4x+1$$, $$g(x) = \dfrac{x}{x-2}$$, and $$h(x) = \sqrt{x+3}$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$4\left(\dfrac{x}{x-2}\right) + 1$$

Question 17

If $$f(x) = |x|$$, what is the effect of the transformation $$y = 3|x|$$?

Accepted Answer

Vertical stretch by a factor of 3

Question 18

Given $$f(x) = \sqrt{x-2}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$[2, \infty)$$

Question 19

If $$f(x) = x^2$ and g(x) = x+1$, what is the value of (f$$ \circ g)(2)$$?

Accepted Answer

$$9$$

Question 20

Which of the following best describes the transformation $$y = f(x) - c$$ for $$c \u003e 0$$?

Accepted Answer

Vertical shift downward by $$c$$ units

Study Guide: Transformations and Algebra of Functions in Precalculus

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