Question 1

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

Accepted Answer

All real numbers except $$x = 3$$

Question 2

A pharmaceutical company models the concentration of a drug in the bloodstream over time with $$C(t) = 5e$$^{-0.2t}$$. What is the concentration after 10 hours?

Accepted Answer

$$C(10) = 5e$$^{-2}$$ \approx 0.676$$

Question 3

Which of the following is the inverse function of $$f(x) = 2x + 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-5}{2}$$

Question 4

A company’s profit $$P is $$modeled by $$P(x) = -2x^2$ + 12x - 16$$, where $$x is $$the number of units sold. What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$P(4) = 8 at$$ $$x = 4$$ units

Question 5

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

Accepted Answer

$$x = 5$$

Question 6

If $$f(x) = x^2$ - 4x + 7$$ and $$g(x) = 3x - 2$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$(f \circ g)(x) = (3x-2)^2$ - 4(3x-2) + 7$$

Question 7

Which of the following is the correct factorization of $$x^2 - 9x + 20$?

Accepted Answer

$$(x-4)(x-5)$$

Question 8

A population of bacteria grows according to $$P(t) = 1000 \cdot 2$$^{t}$$, where t$ is in hours. How many bacteria will there be after 3 hours?

Accepted Answer

$$P(3) = 1000 \cdot 2$$^{3}$$ = 8000$$

Question 9

Which of the following describes the range of the function $$f(x) = \ln(x)$$?

Accepted Answer

All real numbers

Question 10

The equation $$x^2$$ + $$y^2 = 25$ represents which conic section?

Accepted Answer

Circle

Question 11

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

Accepted Answer

$$b^2 - 4ac$$ \geq 0$$

Question 12

Which of the following is the correct graph for $$y = -x^2$ + 4x - 3$$?

Accepted Answer

A downward-opening parabola with vertex at $$(2, 1)$$

Question 13

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

Accepted Answer

$$2 \u003c x \u003c 3$$

Question 14

If $$f(x) = \sqrt{x-1}$$, what is the domain of $$f$$?

Accepted Answer

$$x \geq 1$$

Question 15

A radioactive substance decays according to $$N(t) = N_0$ e$$^{-kt}$$. If N_0$ = 500$$ and $$k = 0.1$$, how much remains after 20 years?

Accepted Answer

$$N(20) = 500e$$^{-2}$$ \approx 67.7$$

Question 16

Which of the following is the correct solution to $$\log_{2}(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 17

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

Accepted Answer

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

Question 18

Which of the following is the correct solution to the equation $$x^2 - 4x = 0$?

Accepted Answer

$$x = 0 or$$ $$x = 4$$

Question 19

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

Accepted Answer

A relation in which each input has exactly one output

MATH 1200 - Precalculus Algebra: Course Syllabus and Topic Outline Study Guide

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