Question 1

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

Accepted Answer

A relation where each input is paired with exactly one output.

Question 2

A pharmaceutical company models the concentration of a drug in the bloodstream over time using the function $$C(t) = 50e$$^{-0.2t}$$, where C$ is concentration in mg/L and t$ is time in hours. What is the concentration after 5 hours?

Accepted Answer

$$C(5) = 50e$$^{-1}$$ \approx 18.4 mg/L$$

Question 3

Which of the following is the equation of a circle with center at $$(3, -2)$$ and radius $$5$$?

Accepted Answer

$$(x - 3)^2$ + (y + 2)^2$ = 25$$

Question 4

A business uses the function $$R(x) = 100x - 2x^2$ to model revenue, where x$ is the number of units sold. What is the maximum revenue, and how many units should be sold to achieve it?

Accepted Answer

Maximum revenue is $$R(25) = 1250$$ when $$x = 25$$

Question 5

Which of the following is the correct solution to the equation $$2x^2 - 8x + 6 = 0$?

Accepted Answer

$$x = 1 or$$ $$x = 3$$

Question 6

If $$f(x) = x^2$ + 3x$$ and $$g(x) = 2x - 1$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$(f \circ g)(x) = (2x - 1)^2$ + 3(2x - 1)$$

Question 7

A city plans to build a circular park. If the diameter of the park is $$60$$ meters, what is the equation of the circle if the center is at $$(0,0)$$?

Accepted Answer

$$x^2$$ + $$y^2 = 900$

Question 8

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 9

A company’s profit is modeled by $$P(x) = -4x^2$ + 40x - 96$$, where $$x is $$the number of products sold. What is the minimum number of products that must be sold for the company to break even?

Accepted Answer

$$x = 3 or$$ $$x = 8$$

Question 10

Which of the following is the correct simplification of $$\log_2$ 32$$?

Accepted Answer

$$\log_2$ 32 = 5$$

Question 11

A line passes through the points $$(2, 3)$$ and $$(6, 11). $$What is the slope of the line?

Accepted Answer

$$m = 2$$

Question 12

Which of the following is the correct solution to the inequality $$x^2 - 5x + 6$$ \u003c 0$$?

Accepted Answer

$$2 \u003c x \u003c 3$$

Question 13

A population of bacteria grows according to $$P(t) = 200e$$^{0.3t}$$, where t$ is in hours. What is the population after 4 hours?

Accepted Answer

$$P(4) = 200e$$^{1.2}$$ \approx 664$$

Question 14

Which of the following is the correct midpoint between the points $$(-4, 6)$$ and $$(2, -2)$$?

Accepted Answer

$$( -1, 2 )$$

Question 15

If $$f(x) = x^2$ - 4x + 7$$, what is the value of $$f(3)$$?

Accepted Answer

$$f(3) = 4$$

Question 16

A chemical reaction is modeled by $$y = 5e$$^{0.5x}$$, where y$ is the concentration and x$ is time in minutes. If the concentration doubles every 1.386$ minutes, what is the value of 0.5x$ when y$ doubles?

Accepted Answer

$$0.5x = \ln 2 \approx 0.693$$

Question 17

Which of the following is the correct solution to the equation $$|2x - 5| = 7$$?

Accepted Answer

$$x = 6 or$$ $$x = -1$$

Question 18

A rational function is given by $$f(x) = \frac{2x + 3}{x - 4}. $$What is the domain of $$f(x)$$?

Accepted Answer

All real numbers except $$x = 4$$

Question 19

Which of the following is the correct property of logarithms for simplifying $$\log_b (xy)$$?

Accepted Answer

$$\log_b (xy) = \log_b x + \log_b y$$

Pre-Calculus Mathematics I: Course Syllabus and Content Overview

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