Question 1

Which of the following equations represents a function? Justify your answer.

Accepted Answer

$y = \sqrt{x}$

Question 2

Given the equation $6x + 2y = 4$, what are the $x$- and $y$-intercepts?

Accepted Answer

$x$-intercept: $(\frac{2}{3}, 0)$, $y$-intercept: $(0, 2)$

Question 3

Solve for $b$ in the equation $\frac{b-1}{2} = b$.

Accepted Answer

$b = -1$

Question 4

Given $f(x) = 2x^2 + 7x + 3$, $g(x) = \sqrt{2x + 1}$, $h(x) = 12$, and $k(x) = \frac{1}{x}$, compute $f(1) + g(12) + h(0) + k(2)$.

Accepted Answer

$12 + 5 + 12 + 0.5 = 29.5$

Question 5

What is the domain of $g(x) = \sqrt{2x + 1}$?

Accepted Answer

$x \geq -0.5$

Question 6

Find all real zeros of $f(x) = 2x^2 + 7x + 3$.

Accepted Answer

$x = -3,\ x = -0.5$

Question 7

Write the equation of a line with $y$-intercept $3$ and $x$-intercept $2$.

Accepted Answer

$y = -\frac{3}{2}x + 3$

Question 8

John rents a car for $200 plus $0.20 per mile driven. Which function models the total cost $C$ for $m$ miles, and what is the cost for 350 miles?

Accepted Answer

$C(m) = 200 + 0.2m;\ C(350) = 270$

Question 9

An oil company increased production from 1.3 million barrels in 2012 to 1.6 million barrels in 2015. What is the average rate of change per year?

Accepted Answer

$0.1$ million barrels per year

Question 10

Suppose India purchased 32,000 industrial robots in 2016, which is 60% more than the US purchased that year. How many did the US purchase?

Accepted Answer

$20,000$

Question 11

Two trains leave a station: the first at 9am at $60$ km/h, the second at 11am at $80$ km/h. At what time will the second train catch up to the first?

Accepted Answer

5pm

Question 12

Two runners, Alex and Brady, start on opposite ends of a $30$ km trail. Alex runs at $9$ km/h, Brady at $7$ km/h. How far will Alex have run when they meet?

Accepted Answer

$16.875$ km

Question 13

Solve the inequality $4|3x - 1| \leq 16$ and write your answer in interval notation.

Accepted Answer

$[-1.25, 1.25]$

Question 14

Given $k(x) = \frac{1}{x}$, what is the domain of $k(x)$?

Accepted Answer

$x 
eq 0$

Question 15

Find the equation of a line with slope $2$ and $x$-intercept $6$.

Accepted Answer

$y = 2x - 12$

Question 16

Given $g(x) = \sqrt{2x + 1}$, find all real zeros of $g(x)$.

Accepted Answer

$x = -0.5$

Question 17

Solve for $x$: $2(x-1) - 2(x-1) = 0$.

Accepted Answer

All real numbers

Question 18

Given $h(x) = 12$, $g(x) = \sqrt{2x + 1}$, and $k(x) = \frac{1}{x}$, compute $k(g(h(9)))$.

Accepted Answer

$\frac{1}{5}$

Question 19

Solve the inequality $\frac{|x + 1|}{3} + 2 > 305$.

Accepted Answer

$x > 902$ or $x < -904$

Question 20

Write the equation for a function $g(x)$ such that $g(3) = 16$ and $g(1) = 5$, assuming $g(x)$ is linear.

Accepted Answer

$g(x) = 5.5x - 0.5$

College Algebra Exam I Practice Guidance

Study Guide - Practice Questions

Study Guide - Flashcards