Q: A medication's concentration in the bloodstream decreases by 20% every hour. If the initial concentration is 100 mg/L, what is the concentration after 3 hours?

$$100 \times 0.8^3$ = 51.2 mg/L$$

Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{5 - 2x}$$?

Accepted Answer

$$x \leq 2.5$$

Question 2

A company models its profit $$P (in $$thousands of dollars) as a function of the number of units sold $$x by$$ $$P(x) = -2x^2$ + 40x - 100. $$What is the maximum profit, and how many units must be sold to achieve it?

Accepted Answer

Maximum profit is $$300 at$$ $$x = 20$$

Question 3

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

Accepted Answer

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

Question 4

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

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

Question 5

Which of the following graphs represents a function that is one-to-one?

Accepted Answer

A straight line with positive slope

Question 6

Solve the inequality $$2x - 5 \u003c 7$$ and select the correct solution set.

Accepted Answer

$$x \u003c 6$$

Question 7

Given the piecewise function $$f(x) = \begin{cases} x^2$ & x \u003c 0 \ 2x + 1 & x \geq 0 \end{cases}$$, what is $$f(-3) + f(2)$$?

Accepted Answer

$$10$$

Question 8

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

Accepted Answer

$$x = 32$$

Question 9

A medication's concentration in the bloodstream decreases by 20% every hour. If the initial concentration is 100 mg/L, what is the concentration after 3 hours?

Accepted Answer

$$100 	imes 0.8^3$ = 51.2 mg/L$$

Question 10

Which of the following is the correct solution to the rational equation $$\frac{2}{x} = 5$$?

Accepted Answer

$$x = 0.4$$

Question 11

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

Accepted Answer

$$9$$

Question 12

Which transformation is applied to the graph of $$y = x^2$ to obtain y = (x$$ - $$3)^2 + 2$?

Accepted Answer

Shift right 3 units and up 2 units

Question 13

A chemical reaction's rate $$R (in $$mol/L/s) is modeled by $$R(t) = 50e$$^{-0.2t}$$, where t$ is time in seconds. What is the rate after 5 seconds? (Round to the nearest whole number.)

Accepted Answer

$$18$$

Question 14

Which of the following is the correct solution to the quadratic equation $$x^2 - 6x + 5 = 0$?

Accepted Answer

$$x = 1$$ and $$x = 5$$

Question 15

Which of the following best describes the range of the function $$f(x) = 2x + 7$$?

Accepted Answer

All real numbers

Question 16

A car rental company charges a flat fee of $$\30$ plus $$\$$0.20$$ per mile driven. Which function models the total cost $$C$$ for $$m$$ miles?

Accepted Answer

$$C(m) = 30 + 0.2m$$

Question 17

Which of the following is the correct solution to the equation $$2^{x} = 16$?

Accepted Answer

$$x = 4$$

Question 18

If $$f(x) = \frac{1}{x}$$, which of the following is the domain of $$f$$?

Accepted Answer

All real numbers except $$x = 0$$

Question 19

A business finds that its revenue $$R in $$dollars from selling $$x$$ units is $$R(x) = 100x - 0.5x^2$. What is the maximum revenue, and at how many units sold does it occur?

Accepted Answer

Maximum revenue is $$5,000 at$$ $$x = 100$$

Question 20

Which of the following is the correct solution to the equation $$\frac{x+2}{x-1} = 3$$?

Accepted Answer

$$x = 2$$

Study Guide: College Algebra Syllabus and Core Topics Overview

Study Guide - Practice Questions

Study Guide - Flashcards