Question 1

Given the mapping diagram below, is the relation a function? What are the domain and range?

$$\begin{array}{c|c}
8 & 1 \
6 & 3 \
4 & 5 \
2 & 3 \
\end{array}

A $$function assigns each input to exactly one output.

Accepted Answer

Yes; Domain: $$\{2, 4, 6, 8\}$$; Range: $$\{1, 3, 5\}$$

Question 2

Consider the graph of a circle centered at the origin with radius 3. Is this relation a function? What is the domain and range?

Accepted Answer

No; Domain: $$[-3, 3]$$; Range: $$[-3, 3]$$

Question 3

Given the piecewise linear graph below, is the relation a function? What is the domain and range?

(The graph passes the vertical line test everywhere.)

Accepted Answer

Yes; Domain: $$(-\infty, \infty)$$; Range: $$(-\infty, 5]$$

Question 4

Let $$f(x) = x^2$ - 1. Is$$ $$f(x) a $$linear function? What is $$f(-2)$$?

Accepted Answer

No; $$f(-2) = 3$$

Question 5

Let $$f(x) = 4x + 7. Is$$ $$f(x) a $$linear function? What is $$f(-2)$$?

Accepted Answer

Yes; $$f(-2) = -1$$

Question 6

Are the lines $$2y = 3x + 2$$ and $$2x + 4y = 5$$ parallel, perpendicular, or neither? Justify your answer.

Accepted Answer

Neither; their slopes are $$\frac{3}{2}$$ and $$-\frac{1}{2}$$

Question 7

Which line is steeper: $$y = \frac{1}{2}x - 7 or$$ $$y = 3x + 5$$? Explain why.

Accepted Answer

$$y = 3x + 5$$; because $$|3| \u003e |\frac{1}{2}|$$

Question 8

Given the table of values:

$$\begin{array}{c|c}
x & y \
1 & 1.5 \
3 & 0.5 \
6 & -1 \
10 & -3 \
\end{array}$$

What is the slope of the linear function that fits this data?

Accepted Answer

$$m = -0.5$$

Question 9

Write the equation in slope-intercept form for a line with slope $$\frac{3}{4}$$ and $$y-$$intercept $$7.$$

Accepted Answer

$$y = \frac{3}{4}x + 7$$

Question 10

Find the equation of the line through the point $$(4, -2)$$ with slope $$3.$$

Accepted Answer

$$y = 3x - 14$$

Question 11

Find the equation of the line passing through $$(-2, 5)$$ and $$(1, 2).$$

Accepted Answer

$$y = -x + 3$$

Question 12

Find the equation of the line passing through $$(1, -1)$$ and perpendicular to $$y = \frac{1}{2}x - 3.$$

Accepted Answer

$$y = -2x + 1$$

Question 13

Given $$f(x) = 3x - 2$$, $$g(x) = \frac{2}{3}x^2$, and h(x$$) = \sqrt{x}$$, find (g + f)(3$$)$$. Simplify completely.

Accepted Answer

$$13$$

Question 14

Given $$f(x) = 3x - 2$$, $$g(x) = \frac{2}{3}x^2$, and h(x$$) = \sqrt{x}$$, find g(h(9$$))$$. Simplify completely.

Accepted Answer

$$6$$

Question 15

What is the domain of $$w(x) = \frac{2}{x-4}$$? Express your answer in interval notation.

Accepted Answer

$$(-\infty, 4) \cup (4, \infty)$$

Question 16

A rideshare service charges a flat pick-up fee of $$3.50 plus 1.75$ for every mile traveled. Write a linear function C(m$$)$$ that models the total cost of a ride as a function of the distance m$ in miles.

Accepted Answer

$$C(m) = 1.75m + 3.50$$

Question 17

A food truck owner purchases a commercial espresso machine for $$6,200. For tax purposes, the machine's value depreciates at a constant rate of 450 $$per year until its value reaches zero. Write a linear model $$V(t)$$ that calculates the value of the espresso machine after $$t$$ years.

Accepted Answer

$$V(t) = 6200 - 450t$$

Functions, Domain, and Range – College Algebra Study Guidance

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