Question 1

Given the function $$f(x) = 3x^2$ + 6x + 2$$, what is the vertex of the parabola?

Accepted Answer

$$(-1, 2)$$

Question 2

Which of the following describes the end behavior of $$f(x) = -4x^3$ + 2x^2$ + x + 1$$?

Accepted Answer

Rises to the left, falls to the right

Question 3

Find the inverse of the function $$f(x) = -8x + 8.$$

Accepted Answer

$$f^{-1}(x$$) = \frac{x-8}{-8}$$

Question 4

Given $$f(x) = x^2$ - 4$$ and $$g(x) = 6x + 3$$, find $$(f+g)(x). $$

Accepted Answer

$$x^2 + 6x - 1$

Question 5

Which of the following functions is even?

Accepted Answer

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

Question 6

Given $$f(x) = x^2$ - 4$$ and $$g(x) = 6x + 3$$, find $$(f \circ g)(x).$$

Accepted Answer

$$(6x+3)^2 - 4$

Question 7

Which of the following is the correct difference quotient for $$f(x) = 3x^2$?

Accepted Answer

$$6x + 3h$$

Question 8

If $$f(x) = x^2$ - 4$$ and $$g(x) = 6x + 3$$, find $$(f-g)(x).$$

Accepted Answer

$$x^2 - 6x - 7$

Question 9

Given the polynomial $$f(x) = 3x^2$(x-3)(x+1)$$, what are the zeros and their multiplicities?

Accepted Answer

$$x=0 ($$multiplicity 2), x=3, x=-1$

Question 10

Which transformation shifts the graph of $$f(x)$$ two units down?

Accepted Answer

$$f(x) - 2$$

Question 11

Given $$f(x) = x^2$ - 4$$ and $$g(x) = 6x + 3$$, find $$(f \cdot g)(x).$$

Accepted Answer

$$(x^2 - 4)(6x + 3$$)$$

Question 12

Which of the following is the correct inverse for $$f(x) = \frac{3x}{x+1}$$?

Accepted Answer

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

Question 13

Which of the following intervals represents the domain of $$f(x) = \sqrt{x+3}$$?

Accepted Answer

$$[-3, \infty)$$

Question 14

Given $$f(x) = x^2$ - 4$$ and $$g(x) = 6x + 3$$, find $$(f/g)(x).$$

Accepted Answer

$$\frac{x^2$ - 4}{6x + 3}$$

Question 15

Which of the following is the correct set of $$x-$$intercepts for the equation $$y = x^2$ - 36$$?

Accepted Answer

$$(-6, 0)$$ and $$(6, 0)$$

Question 16

Which of the following is the correct difference quotient for $$f(x) = 3x - 7$$?

Accepted Answer

$$3$$

Question 17

Given $$f(x) = x^2$ - 4$$ and $$g(x) = 6x + 3$$, find $$(f \circ g)(1).$$

Accepted Answer

$$49$$

Question 18

Which of the following is the correct $$y-$$intercept for the equation $$y = x^2$ - 36$$?

Accepted Answer

$$(0, -36)$$

Question 19

Which of the following is the correct vertex for $$f(x) = x^2$ + 6x + 13$$?

Accepted Answer

$$(-3, 4)$$

College Algebra Final Exam Study Guide – Key Concepts and Practice Problems

Study Guide - Practice Questions