Question 1

Given the relation $$\{(-2, 3), (0, 3), (2, 4)\}$$, what is the domain and range, and is this relation a function?

Accepted Answer

Domain: $$\{-2, 0, 2\}$$, Range: $$\{3, 4\}$$, and it is a function.

Question 2

Which of the following equations represents a vertical line?

Accepted Answer

$$x = -1$$

Question 3

Evaluate the function $$f(x) = 3 + x at$$ $$x = 0.$$

Accepted Answer

$$f(0) = 3$$

Question 4

Which of the following graphs passes the vertical line test and represents a function?

Accepted Answer

A graph where every vertical line intersects the graph at most once.

Question 5

Given $$f(x) = -x^3$ + 2x + 4$$ and $$g(x) = 4x - 6$$, what is $$(f+g)(x)$$?

Accepted Answer

$$(f+g)(x) = -x^3$ + 6x - 2$$

Question 6

What is the slope of the line passing through the points $$(0, -4)$$ and $$(-9, -1)$$?

Accepted Answer

$$m = \frac{-1 - (-4)}{-9 - 0} = \frac{3}{-9} = -\frac{1}{3}$$

Question 7

Write the equation of a line in point-slope form with a slope of $$\frac{1}{2}$$ that passes through the point $$(1, -4).$$

Accepted Answer

$$y + 4 = \frac{1}{2}(x - 1)$$

Question 8

Given the line $$y = -5x + 6$$, what is the slope and y-intercept?

Accepted Answer

Slope: $$-5$$, y-intercept: $$6$$

Question 9

Find the equation of the line passing through $$(0, -5)$$ and $$(2, 7) in $$slope-intercept form.

Accepted Answer

$$y = 6x - 5$$

Question 10

Which of the following describes the relationship between the graphs of $$f(x) = x^2$ and g(x$$) = $$(x+1)^2$$?

Accepted Answer

The graph of $$g(x) is $$the graph of $$f(x)$$ shifted 1 unit to the left.

Question 11

If two lines are perpendicular and one has slope $$m_1 = 2$, what is the slope m_2$ of the other?

Accepted Answer

$$m_2$$ = -\frac{1}{2}$$

Question 12

Write the equation of a line that passes through $$(-1, 4)$$ and is parallel to $$x + 2y = 5.$$

Accepted Answer

$$x + 2y = 9$$

Question 13

Which of the following is the correct domain for the function $$f(x) = -x^3$ + 2x + 4$$?

Accepted Answer

All real numbers

Question 14

Given $$f(x) = -2$$, what is the slope and y-intercept of the line?

Accepted Answer

Slope: $$0$$, y-intercept: $$-2$$

Question 15

A company’s online advertising revenue increases by $$5$$ billion dollars each year, starting at $$5$$ billion in 2008. Which equation models the revenue $$y in $$year $$x$$, where $$x=0$$ corresponds to 2008?

Accepted Answer

$$y = 5x + 5$$

Question 16

Which of the following is the equation of a line perpendicular to $$y = 2x + 3$$ with a y-intercept of $$10$$?

Accepted Answer

$$y = -\frac{1}{2}x + 10$$

Question 17

Find the x-intercept of the line $$3x + 4y = 12.$$

Accepted Answer

$$(4, 0)$$

Question 18

Which of the following is NOT a function?

Accepted Answer

A relation where a single x-value is paired with two different y-values.

Question 19

Given $$f(x) = -x^3$ + 2x + 4$$ and $$g(x) = 4x - 6$$, what is $$(f \cdot g)(x)$$?

Accepted Answer

$$(f \cdot g)(x) = (-x^3$ + 2x + 4)(4x - 6)$$

Intermediate Algebra: Functions, Graphs, and Lines Study Guide

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