Question 1

If the point $(5, 55)$ lies on the graph of $f$, then $f(5) = $ ____.

Accepted Answer

$55$

Question 2

Given the function $f(x) = \frac{1}{2}x + 4$, what is the $y$-intercept of the graph?

Accepted Answer

$4$

Question 3

Evaluate $g(a + 1)$ when $g(x) = 4x - 2$.

Accepted Answer

$4a + 2$

Question 4

Specify the domain of the function $f(x) = \frac{x}{x-4}$.

Accepted Answer

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

Question 5

A cab ride costs $y = 3.14 + 1.43x$, where $x$ is the number of miles. What is the cost of a 4-mile cab ride?

Accepted Answer

$8.86$

Question 6

Determine if the relation given by the set $\{(-3, 1), (-2, 1.3), (-1, 2.4), (0, -2.7), (1, -4.0), (2, -1.4)\}$ is a function.

Accepted Answer

Yes, because each $x$-value is paired with exactly one $y$-value.

Question 7

Bob buys a car that gets 18 miles per gallon of gasoline. Which function represents the number of miles $y$ that Bob can travel with $x$ gallons of gasoline?

Accepted Answer

$y = 18x$

Question 8

Find the slope of the line that passes through the points $(5, -3)$ and $(7, -2)$.

Accepted Answer

$\frac{1}{2}$

Question 9

The decline in the value of a stock can be estimated by the function $f(x) = -0.61x + 1289.9$, where $x$ is the year with 1990 as $x = 2000$. What is the slope of the graph of $f$ and what does it represent?

Accepted Answer

The slope is $-0.61$ and it represents the average decrease in value per year.

Question 10

Given the equation $4(x + 20) = \frac{1}{2}(x - 12)$, what is the solution for $x$?

Accepted Answer

$x = -28$

Question 11

A chemistry class needs to mix 3 liters of a 4% silver iodide solution with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

Accepted Answer

$1$

Question 12

Find the length of a rectangular lot with a perimeter of $140$ m if the length is $6$ m more than the width.

Accepted Answer

$38$ m

Question 13

Solve the inequality $-3(2x - 5) \leq 9x + 24$ and express the solution set in interval notation.

Accepted Answer

$(-\infty, -3]$

Question 14

Factor the expression $x^2 + 8x + 16$ completely.

Accepted Answer

$(x + 4)^2$

Question 15

Express the set $(-\infty, 2]$ in interval notation as shown on the number line.

Accepted Answer

$(-\infty, 2]$

Question 16

Write the equation of the line passing through $(2, 5)$ with slope $-2$ in slope-intercept form.

Accepted Answer

$y = -2x + 9$

Question 17

If $f(x) = 5x - 1$, for which interval is $f$ increasing?

Accepted Answer

$(-\infty, \infty)$

Question 18

The cost for labor associated with fixing a washing machine is computed as follows: There is a fixed charge of $25 for the repairman to come to the house, to which a charge of $29 per hour is added. Which equation gives the total labor cost $C(t)$ for $t$ hours?

Accepted Answer

$C(t) = 29t + 25$

Question 19

Factor the expression $42 - 17x - 6x^2$ completely.

Accepted Answer

$-(3x + 14)(2x - 3)$

Question 20

Given the piecewise function $f(x) = \left\{ \begin{array}{ll} x - 5 & x \geq 0 \ -3 & x < 0 \end{array} ight.$, what is $f(-2)$?

Accepted Answer

$-3$

College Algebra: Functions, Equations, Graphs, and Applications Study Guide

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