Question 1

Which of the following best describes the domain of the function $$f(x) = \dfrac{1}{x-3}$$?

Accepted Answer

$$x 
eq 3$$

Question 2

A biologist models the population of a bacteria colony with the exponential function $$P(t) = 500e$$^{0.2t}$$, where t$ is measured in hours. What is the approximate population after 5 hours?

Accepted Answer

$$P(5) \approx 500e$$^{1}$$ \approx 1359$$

Question 3

Which of the following is the correct equation for the line passing through the points $$(2, 5)$$ and $$(6, 13)$$?

Accepted Answer

$$y = 2x + 1$$

Question 4

Given the quadratic function $$f(x) = x^2$ - 6x + 8$$, what are its zeros?

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 5

A pharmaceutical company models the decay of a drug in the bloodstream by $$C(t) = 100e$$^{-0.3t}$$, where C$ is the concentration in mg/L and t$ is time in hours. What is the half-life of the drug?

Accepted Answer

$$t = \dfrac{\ln 2}{0.3} \approx 2.31$$ hours

Question 6

Which of the following transformations will shift the graph of $$f(x) = x^2$ two units to the right and three units up?

Accepted Answer

$$f(x) = (x-2)^2$ + 3$$

Question 7

A chemical reaction follows the logistic growth model $$N(t) = \dfrac{500}{1 + 9e$$^{-0.5t}$$}. $$What is the limiting value of $$N(t) as$$ $$t 	o \infty$$?

Accepted Answer

$$500$$

Question 8

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

Accepted Answer

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

Question 9

A parabola has its vertex at $$(4, -2)$$ and opens upward. Which of the following could be its equation?

Accepted Answer

$$y = (x-4)^2$ - 2$$

Question 10

Which of the following is the correct solution to the inequality $$2x - 5 \u003c 9$$?

Accepted Answer

$$x \u003c 7$$

Question 11

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P(x) = -2x^2$ + 12x - 16$$, 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 $$P(3) = 10$$ thousand dollars, at $$x = 3$$ thousand units

Question 12

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

Accepted Answer

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

Question 13

Given the rational function $$f(x) = \dfrac{x^2$ - 9}{x^2$ - 4}$$, which values of $$x$$ are excluded from the domain?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 14

A hospital monitors the temperature of a patient using the function $$T(t) = 98.6 + 1.2\sin(\pi t)$$, where $$t is in $$hours. What is the maximum temperature recorded?

Accepted Answer

$$99.8^\circF$$

Question 15

Which of the following is the solution set for the system of equations: $$\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$(x, y) = (3, 2)$$

Question 16

Which of the following is the correct binomial expansion for $$(x + 2)^3$?

Accepted Answer

$$x^3$$ + $$6x^2 + 12x + 8$

Question 17

A scientist uses the function $$f(x) = \log_{10}(x) to $$model the pH of a solution. If the hydrogen ion concentration is $$x = 0.001$$, what is the pH?

Accepted Answer

$$f(0.001) = -3$$

Question 18

Which of the following is the correct solution to the exponential equation $$2^{x} = 32$?

Accepted Answer

$$x = 5$$

Question 19

A business models its revenue with $$R(x) = 4x^2$ - 20x + 25. $$What is the minimum revenue, and at what value of $$x$$ does it occur?

Accepted Answer

Minimum revenue is $$R(2.5) = 0$$, at $$x = 2.5$$

Precalculus Syllabus and Course Information – Key Concepts and Study Guide

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