Q: Which of the following best describes the end behavior of the function $$f(x) = -2x^4$ + 5x^2$ - 3$$?

As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to -\infty.$$

Q: A car depreciates in value according to the function $$V(t) = 25000(0.85)^t$$, where $$t is $$the number of years. What is the value of the car after 3 years?

$$25000 \times (0.85)^3$ \approx 15306.25$$

Question 1

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

Accepted Answer

A function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

Question 2

Given the polynomial $$f(x) = x^3$ - 4x^2$ + x + 6$$, which of the following is a possible rational zero according to the Rational Root Theorem?

Accepted Answer

$$2$$

Question 3

Which of the following best describes the end behavior of the function $$f(x) = -2x^4$ + 5x^2$ - 3$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o -\infty.$$

Question 4

A hospital uses the exponential decay model $$N(t) = N_0$ e$$^{-kt}$$ to predict the amount of a drug in a patient’s bloodstream. If N_0$ = 100 mg $$and $$k = 0.2$$, how much drug remains after 5 hours?

Accepted Answer

$$100 e$$^{-1}$$ mg \approx 36.79$ mg

Question 5

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 6

A population of bacteria doubles every 3 hours. If the initial population is 500, what will the population be after 9 hours?

Accepted Answer

$$500 	imes 2^3$ = 4000$$

Question 7

Which of the following is NOT a characteristic of exponential functions?

Accepted Answer

The graph always passes through the origin.

Question 8

Solve the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$

Accepted Answer

$$x = 2, y = 1$$

Question 9

Which of the following describes the domain of the function $$f(x) = \frac{1}{x^2$ - 4}$$?

Accepted Answer

All real numbers except $$x = 2$$ and $$x = -2$$

Question 10

A company’s revenue $$R (in $$thousands of dollars) is modeled by $$R(x) = -2x^2$ + 40x$$, where $$x is $$the number of units sold. What is the maximum revenue, and how many units must be sold to achieve it?

Accepted Answer

Maximum revenue is $$400 at$$ $$x = 10$$

Question 11

Which of the following is the correct factorization of $$x^2 - 5x + 6$?

Accepted Answer

$$(x - 2)(x - 3)$$

Question 12

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

Accepted Answer

$$f(g(2)) = f(3) = 9$$

Question 13

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

Accepted Answer

$$x = 32$$

Question 14

A radioactive substance decays according to $$A(t) = 200e$$^{-0.3t}$$. How much remains after 4 hours?

Accepted Answer

$$200e^{-1.2}$$ \approx 60.22$$

Question 15

Which of the following is the correct equation for the horizontal asymptote of $$f(x) = \frac{3x^2$ + 2}{x^2$ - 5}$$?

Accepted Answer

$$y = 3$$

Question 16

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

Accepted Answer

$$(2, 3)$$

Question 17

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

Accepted Answer

$$x = 4$$

Question 18

A car depreciates in value according to the function $$V(t) = 25000(0.85)^t$$, where $$t is $$the number of years. What is the value of the car after 3 years?

Accepted Answer

$$25000 	imes (0.85)^3$ \approx 15306.25$$

Question 19

Which of the following is the correct solution to the quadratic equation $$x^2 + 6x + 9 = 0$?

Accepted Answer

$$x = -3$$

Precalculus Syllabus and Study Guide: MTH 161 - V04 Spring 2026

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