Question 1

Which of the following is the correct domain of the function $$g(x) = \sqrt{6 - 2x}$$?

Accepted Answer

$$x \leq 3$$

Question 2

Given the relation $$\{(2, 5), (3, 6), (2, 7), (3, 8)\}$$, is this relation a function?

Accepted Answer

No, because the $$x-$$values repeat with different $$y-$$values.

Question 3

For the function $$f(x) = \frac{x-2}{x+3}$$, which of the following describes its vertical asymptote?

Accepted Answer

$$x = -3$$

Question 4

Given the piecewise function $$f(x) = \begin{cases} 3x + 5 & x \u003c -1 \ x^2$ - 4 & -1 \leq x \leq 3 \ 1 - 3x & 3 \u003c x \end{cases}$$, what is $$f(5)$$?

Accepted Answer

$$-14$$

Question 5

A salesperson earns a base pay of $$130 per week plus a commission of 9$ for every item sold. Which equation models her weekly salary S$ as a function of the number of items n$ sold?

Accepted Answer

$$S = 130 + 9n$$

Question 6

Find the difference quotient $$\frac{f(x+h) - f(x)}{h}$$ for $$f(x) = 2x^2$ - 6. $$Simplify your answer.

Accepted Answer

$$4x + 2h$$

Question 7

Which of the following graphs represents a function?

Accepted Answer

A graph that passes the vertical line test everywhere.

Question 8

Given the quadratic function $$y = x^2$ + 2x - 6$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = -3, x = 2$$

Question 9

Write the equation of a line passing through the points $$(5, -2)$$ and $$(2, -2).$$

Accepted Answer

$$y = -2$$

Question 10

For the function $$f(x) = (x + 4)^2$ - 3$$, what is the vertex of the graph?

Accepted Answer

$$(-4, -3)$$

Question 11

Given $$f(x) = (x + 4)^2$ - 3$$, what is the axis of symmetry?

Accepted Answer

$$x = -4$$

Question 12

Find all real and non-real zeros of the polynomial $$f(x) = x^4$ + 3x^2$ + 4x + 12.$$

Accepted Answer

There are no real zeros; all zeros are non-real complex numbers.

Question 13

Given the graph of $$y = f(x)$$, which interval is $$f$$ increasing?

Accepted Answer

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

Question 14

Given $$f(x) = x^2$ + 2x - 6$$, what is the axis of symmetry?

Accepted Answer

$$x = -1$$

Question 15

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

Accepted Answer

$$g(x) = (x - 3)^2$ + 3$$

Question 16

Given the function $$y = 5 - x$$, which of the following is true?

Accepted Answer

The graph is a straight line with slope $$-1$$ and $$y-$$intercept $$5.$$

Question 17

For the quadratic $$y = x^2$ + 2x - 6$$, what is the minimum value of the function?

Accepted Answer

$$-7$$

Question 18

Given the function $$h(x) = 2x^2$ - 2$$, what is the $$y-$$intercept?

Accepted Answer

$$-2$$

Question 19

Which of the following best describes the graph of $$y = x^2$ + 2x - 6$$?

Accepted Answer

A parabola opening upwards with vertex at $$(-1, -7).$$

Question 20

If $$R(p) = -6p^2$ + 90p$$ models the revenue $$R as a $$function of the price $$p in $$dollars of a product, what price maximizes the revenue?

Accepted Answer

$$p = 7.5$$

College Algebra: Functions, Graphs, and Applications Study Guide

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