Q: A company’s profit $P$ (in thousands of dollars) is modeled by $P(x) = -2x^2 + 12x - 9$, where $x$ is the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Maximum profit is $15$ thousand dollars at $x = 3$ thousand units.

Q: Which of the following is the inverse of the function $f(x) = 3x + 7$?

$f^{-1}(x) = \displaystyle \frac{x-7}{3}$

Question 1

Which of the following is the correct definition of a polynomial function?

Accepted Answer

A function that can be written in the form $f(x) = a_n x^n + a_{n-1} x^{n-1} + \ldots + a_1 x + a_0$, where all coefficients $a_i$ are real numbers and $n$ is a non-negative integer.

Question 2

A pharmaceutical company models the concentration of a drug in the bloodstream over time with the function $C(t) = 50e^{-0.2t}$, where $C$ is in mg/L and $t$ is in hours. What type of function is this, and what is its domain?

Accepted Answer

Exponential function; domain is all real numbers $t \geq 0$

Question 3

Which of the following equations represents a rational inequality?

Accepted Answer

$\displaystyle \frac{x+2}{x-3} > 0$

Question 4

Given the piecewise function

$\displaystyle f(x) = \begin{cases} x^2, & x < 0 \ 2x + 1, & x \geq 0 \end{cases}$

What is $f(-3) + f(2)$?

Accepted Answer

$9 + 5 = 14$

Question 5

A company’s profit $P$ (in thousands of dollars) is modeled by $P(x) = -2x^2 + 12x - 9$, where $x$ is the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $15$ thousand dollars at $x = 3$ thousand units.

Question 6

Which of the following is the inverse of the function $f(x) = 3x + 7$?

Accepted Answer

$f^{-1}(x) = \displaystyle \frac{x-7}{3}$

Question 7

Solve the following system of equations using matrices:

$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$

Accepted Answer

$x = 2,\ y = 1$

Question 8

Which of the following best describes the domain of the function $f(x) = \sqrt{5 - x}$?

Accepted Answer

$x \leq 5$

Question 9

A population of bacteria triples every 4 hours. If the initial population is 200, which equation models the population $P$ after $t$ hours?

Accepted Answer

$P = 200 \cdot 3^{t/4}$

Question 10

Which of the following is the solution set for the inequality $|2x - 5| < 7$?

Accepted Answer

$-1 < x < 6$

Question 11

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

Accepted Answer

$21$

Question 12

Which of the following is the correct solution to the equation $\log_2(x) = 5$?

Accepted Answer

$x = 32$

Question 13

A quadratic equation $ax^2 + bx + c = 0$ has real and distinct roots if:

Accepted Answer

$b^2 - 4ac > 0$

Question 14

Which of the following is the sum of the first 5 terms of the arithmetic sequence where $a_1 = 3$ and $d = 4$?

Accepted Answer

$55$

Question 15

A conic section is defined by the equation $x^2 + 4y^2 = 16$. What type of conic is this, and what are its axes lengths?

Accepted Answer

Ellipse; axes lengths are $4$ and $2$

Question 16

A student invests $\$1000$ in an account that earns $6\%$ annual interest compounded quarterly. Which formula gives the amount $A$ after $t$ years?

Accepted Answer

$A = 1000 \left(1 + \frac{0.06}{4}\right)^{4t}$

Question 17

Which of the following is the correct domain for the function $f(x) = \displaystyle \frac{2x+1}{x^2 - 9}$?

Accepted Answer

$x 
eq 3,\ x 
eq -3$

Question 18

If $f(x) = 2x - 1$ and $g(x) = x^2$, what is $f(g(2))$?

Accepted Answer

$7$

Question 19

A lottery has 5 winning tickets out of 1000. What is the probability of buying a single ticket and winning?

Accepted Answer

$\displaystyle \frac{1}{200}$

College Algebra Syllabus and Course Overview – MATH 1314

Study Guide - Practice Questions

Study Guide - Flashcards