Question 1

Which of the following is the correct domain of the function $$g(x) = \frac{x+1}{x+2}$$?

Accepted Answer

$$(-\infty, -2) \cup (-2, \infty)$$

Question 2

Given $$f(x) = x^2$ + 3x$$, what is $$f(3)$$?

Accepted Answer

$$18$$

Question 3

If $$f(x) = x^2$ + 3x$$ and $$g(x) = 2x^2$ + 3x$$, what is $$f(x) + g(x)$$?

Accepted Answer

$$3x^2 + 6x$

Question 4

Given $$f(x) = x^2$ + 9$$ and $$g(x) = 3x + 5$$, what is $$(f+g)(2)$$?

Accepted Answer

$$24$$

Question 5

Given $$f(x) = x^2$ + 9$$ and $$g(x) = 3x + 5$$, what is $$(f-g)(5)$$?

Accepted Answer

$$14$$

Question 6

If $$f(x) = x^2$ + 3x$$ and $$g(x) = 2x^2$ + 3x$$, what is $$f(x) - g(x)$$?

Accepted Answer

$$-x^2$$

Question 7

Given $$f(x) = x^2$ + 9$$ and $$g(x) = 3x + 5$$, what is $$\frac{f(1)}{g(1)}$$?

Accepted Answer

$$\frac{5}{4}$$

Question 8

If $$g(x) = x^2$ + 3x + 14$$ and $$f(x) = x^2$ + 9$$, what is $$(g-f)(x)$$?

Accepted Answer

$$3x + 5$$

Question 9

Given $$f(x) = x^2$ + 3x$$, calculate $$\frac{f(x+h) - f(x)}{h}$$ for $$h 
eq 0.$$

Accepted Answer

$$2x + 2h + 3$$

Question 10

For the function $$g(x) = \frac{x+1}{x+2}$$, what is the $$x-$$intercept?

Accepted Answer

$$(-1, 0)$$

Question 11

For the function $$g(x) = \frac{x+1}{x+2}$$, what is the $$y-$$intercept?

Accepted Answer

$$(0, 1/2)$$

Question 12

If $$g(x) = \frac{x+1}{x+2}$$ and $$g(x) = 2$$, what is $$x$$?

Accepted Answer

$$x = -4$$

Question 13

Which of the following points is NOT on the graph of $$g(x) = \frac{x+1}{x+2}$$?

Accepted Answer

$$(1, 1/2)$$

Question 14

Given $$f(x) = x^2$ + 3x$$ and $$g(x) = 2x^2$ + 3x$$, what is $$f(x) \cdot g(x)$$?

Accepted Answer

$$2x^4$$ + $$9x^3$$ + $$15x^2 + 9x$

Question 15

If $$f(x) = x^2$ + 9$$ and $$g(x) = 3x + 5$$, what is $$\frac{g(x) - f(x)}{f(x)}$$?

Accepted Answer

$$\frac{3x + 5 - (x^2$ + 9)}{x^2$ + 9}$$

Question 16

Which of the following best describes why $$y = x^2$ + y^2$ = 4 is $$NOT a function?

Accepted Answer

Because $$y is $$raised to an even power, so for some $$x$$ there are multiple $$y$$ values.

Question 17

Given $$f(x) = x^2$ + 3x$$, what is $$f(-2)$$?

Accepted Answer

$$-2$$

Question 18

If $$f(x) = x^2$ + 3x$$ and $$g(x) = 2x^2$ + 3x$$, what is $$f(x) \div g(x)$$?

Accepted Answer

$$\frac{x^2$ + 3x}{2x^2$ + 3x}$$

Question 19

If $$f(x) = x^2$ + 3x$$ and $$g(x) = 2x^2$ + 3x$$, what is $$f(g(x))$$?

Accepted Answer

$$(2x^2$$ + $$3x)^2$$ + $$3(2x^2 + 3x$$)$$

Functions: Definitions, Operations, and Applications

Study Guide - Practice Questions