Q: A quadratic equation models the height $$h (in $$meters) of a ball thrown upward: $$h(t) = -4.9t^2$ + 20t + 2. $$What is the maximum height reached by the ball?

The maximum occurs at $$t = \frac{-b}{2a} = \frac{-20}{2 \times -4.9} \approx 2.04$$ seconds, so $$h(2.04) \approx 22.4$$ meters.

Q: A company’s revenue is modeled by $$R(x) = -2x^2$ + 40x$$, where $$x is $$the number of units sold. What is the maximum revenue?

Maximum at $$x = \frac{-b}{2a} = \frac{-40}{2 \times -2} = 10$$, so $$R(10) = -2 \times 100 + 40 \times 10 = -200 + 400 = 200$$

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

Given the function $$f(x) = 2x^2$ - 3x + 5$$, what is the domain of $$f$$?

Accepted Answer

All real numbers $$x$$

Question 3

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

Accepted Answer

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

Question 4

A pharmaceutical company models the concentration of a drug in the bloodstream over time with $$C(t) = 50e$$^{-0.2t}$$. What is the concentration after 5 hours?

Accepted Answer

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

Question 5

Which of the following is a real zero of the polynomial $$p(x) = x^2$ - 5x + 6$$?

Accepted Answer

$$x = 2$$

Question 6

A quadratic equation models the height $$h (in $$meters) of a ball thrown upward: $$h(t) = -4.9t^2$ + 20t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

The maximum occurs at $$t = \frac{-b}{2a} = \frac{-20}{2 	imes -4.9} \approx 2.04$$ seconds, so $$h(2.04) \approx 22.4$$ meters.

Question 7

Which of the following is the correct factorization of $$x^3 - 8$?

Accepted Answer

$$(x - 2)(x^2$ + 2x + 4)$$

Question 8

A population of bacteria grows according to $$P(t) = 1000 \cdot 2^t. $$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 graph of $$y = \frac{1}{x}$$?

Accepted Answer

It has a vertical asymptote at $$x = 0$$ and a horizontal asymptote at $$y = 0.$$

Question 10

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

Accepted Answer

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

Question 11

A chemical reaction follows the equation $$y = 5 \ln(x)$$, where $$y is $$the reaction rate and $$x is $$the concentration. If the concentration doubles from $$x = 2 to$$ $$x = 4$$, by how much does the reaction rate increase?

Accepted Answer

Increase is $$5 \ln(4) - 5 \ln(2) = 5 \ln(2) \approx 3.47$$

Question 12

Which of the following is the solution set for the inequality $$x^2 - 4x + 3$$ \u003c 0$$?

Accepted Answer

$$1 \u003c x \u003c 3$$

Question 13

Which of the following is the correct domain for the function $$f(x) = \sqrt{2x - 8}$$?

Accepted Answer

$$x \geq 4$$

Question 14

A company’s revenue is modeled by $$R(x) = -2x^2$ + 40x$$, where $$x is $$the number of units sold. What is the maximum revenue?

Accepted Answer

Maximum at $$x = \frac{-b}{2a} = \frac{-40}{2 	imes -2} = 10$$, so $$R(10) = -2 	imes 100 + 40 	imes 10 = -200 + 400 = 200$$

Question 15

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

Accepted Answer

$$x = 4$$

Question 16

Which of the following is the correct graph for $$y = x^2$ - 6x + 9$$?

Accepted Answer

A parabola opening upwards with vertex at $$(3, 0)$$

Question 17

Which of the following is the correct property of logarithms?

Accepted Answer

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

Question 18

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

Accepted Answer

$$x = 32$$

Precalculus Algebra: Course Syllabus and Topic Overview

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