Question 1

Which of the following equations is symmetric with respect to the y-axis?

Accepted Answer

$$y = x^2$

Question 2

Given the function $$f(x) = x^2$ - 2x$$, what is $$f(2)$$?

Accepted Answer

$$0$$

Question 3

For the function $$f(x) = \sqrt{x-3}$$, what is the domain?

Accepted Answer

$$x \geq 3$$

Question 4

Which of the following is the correct difference quotient for $$f(x) = x^2$?

Accepted Answer

$$\dfrac{(x+h)^2$ - x^2$}{h}$$

Question 5

If $$f(x) = x^2$ - 2x$$ and $$g(x) = 2(x-2x)$$, what is $$f(x) + g(x)$$?

Accepted Answer

$$x^2 - 4x$

Question 6

Given $$f(x) = \dfrac{2x}{x-3}$$ and $$g(x) = \dfrac{x}{x+2}$$, what is the domain of $$f(x) + g(x)$$?

Accepted Answer

$$x 
eq 3, x 
eq -2$$

Question 7

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$

Question 8

A right triangle has a base $$x$$ and height $$3x. $$Express the area $$A(x) as a $$function of $$x$$ and state its domain.

Accepted Answer

$$A(x) = \dfrac{3x^2$}{2},\ x \u003e 0$$

Question 9

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

Accepted Answer

$$-4x$$

Question 10

For the function $$f(x) = \dfrac{3}{x(x+h)}$$, what is the difference quotient $$\dfrac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$\dfrac{-3h}{h x(x+h)}$$

Question 11

Which of the following is NOT a step in testing a function for symmetry with respect to the origin?

Accepted Answer

Replace $$y$$ with $$-y$$ only.

Question 12

Given $$f(x) = x^2$ - 2x$$, what is $$f(x+h) - f(x)$$?

Accepted Answer

$$2xh + h^2$ - 2h$$

Question 13

If $$f(x) = x^2$ - 2x$$, what is the average rate of change of $$f$$ from $$x = 1 to$$ $$x = 4$$?

Accepted Answer

$$5$$

Question 14

For the function $$f(x) = \dfrac{x+3}{x+4}$$, what are the x-intercepts?

Accepted Answer

$$x = -3$$

Question 15

Given $$f(x) = x^2$ - 2x$$ and $$g(x) = x^2$ + 2x$$, what is the domain of $$\dfrac{f(x)}{g(x)}$$?

Accepted Answer

$$x 
eq 0, x 
eq -2$$

Question 16

If $$f(x) = x^2$ - 2x$$, what is $$f(-x)$$?

Accepted Answer

$$x^2 + 2x$

Question 17

Which of the following best describes the range of the function $$f(x) = \sqrt{x-3}$$?

Accepted Answer

$$y \geq 0$$

Question 18

If $$f(x) = x^2$ - 2x$$, for what value(s) of $$x$$ does $$f(x) = 0$$?

Accepted Answer

$$x = 0$$ and $$x = 2$$

Question 19

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

Accepted Answer

$$x^4$$ - $$4x^2$$

Precalculus Study Guide: Symmetry, Functions, Domains, and Operations

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