Q: Which of the following best describes the symmetry of the function $f(x) = x^4 - 2x^2$?

Even; symmetric with respect to the $y$-axis

Question 1

A chemical reaction's temperature $T$ (in degrees Celsius) is modeled by the function $T(t) = 5t^2 - 20t + 30$, where $t$ is the time in hours. What is the minimum temperature reached during the reaction, and at what time does it occur?

Accepted Answer

$T = 10$ at $t = 2$

Question 2

Which of the following relations is a function?

Accepted Answer

$\{ (1,2), (2,3), (3,4) \}$

Question 3

Solve the quadratic equation $x^2 - 6x + 5 = 0$ and select the correct solution set.

Accepted Answer

$\{1, 5\}$

Question 4

A biologist models the population of a bacteria culture by $P(t) = 200 \cdot 2^t$, where $t$ is the number of hours since the start of the experiment. What is the population after 3 hours?

Accepted Answer

$1600$

Question 5

Which of the following equations represents a line perpendicular to $y = -\frac{1}{2}x + 3$?

Accepted Answer

$y = 2x - 1$

Question 6

Solve the absolute value equation $|2x - 5| = 7$.

Accepted Answer

$x = 6,\ x = -1$

Question 7

A company’s profit $P$ (in thousands of dollars) is given by $P(x) = -2x^2 + 8x + 10$, where $x$ is the number of units sold (in thousands). What is the maximum profit, and how many units must be sold to achieve it?

Accepted Answer

$P = 18$ at $x = 2$

Question 8

Which of the following is the correct domain of the function $f(x) = \frac{1}{x-4}$?

Accepted Answer

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

Question 9

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

Accepted Answer

$6$

Question 10

A medication’s concentration in the bloodstream is modeled by $C(t) = 50e^{-0.2t}$, where $t$ is in hours. What is the concentration after 5 hours? (Round to the nearest whole number.)

Accepted Answer

$18$

Question 11

Which of the following functions is even?

Accepted Answer

$f(x) = x^2 + 1$

Question 12

Solve the inequality $2x - 3 < 7$ and express the solution in interval notation.

Accepted Answer

$(-\infty, 5)$

Question 13

A car rental company charges a flat fee of $\$20$ plus $\$0.15$ per mile driven. Which equation models the total cost $C$ for $m$ miles driven?

Accepted Answer

$C = 0.15m + 20$

Question 14

Which of the following intervals represents the range of the function $f(x) = |x - 2|$?

Accepted Answer

$[0, \infty)$

Question 15

If $f(x) = 3x - 4$ and $g(x) = x^2$, what is $(f \circ g)(2)$?

Accepted Answer

$8$

Question 16

A ball is thrown upward from a height of $2$ meters with an initial velocity of $8$ m/s. Its height after $t$ seconds is given by $h(t) = -4.9t^2 + 8t + 2$. After how many seconds does the ball reach its maximum height?

Accepted Answer

$t = 0.82$

Question 17

Which of the following best describes the symmetry of the function $f(x) = x^4 - 2x^2$?

Accepted Answer

Even; symmetric with respect to the $y$-axis

Question 18

Solve the system of equations: $\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$

Accepted Answer

$x = 2,\ y = 3$

Question 19

Which of the following is the solution set for the inequality $|x + 4| \leq 2$?

Accepted Answer

$[-6, -2]$

College Algebra Exam 1 Review: Comprehensive Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards