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

Question 1

Which of the following is the correct end behavior for a polynomial of degree 4 with a positive leading coefficient?

Accepted Answer

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

Question 2

Given the function $$f(x) = \dfrac{3x^2$ + 2x}{2x^2$ - 5x - 3}$$, what is the horizontal asymptote?

Accepted Answer

$$y = \dfrac{3}{2}$$

Question 3

Which of the following statements must be true about a polynomial whose graph starts in quadrant II and ends in quadrant III?

Accepted Answer

The degree is odd and the leading coefficient is negative.

Question 4

What is the solution to $$2^{3x+1}$$ = $$2^{4x-2}$$?

Accepted Answer

$$x = 1.5$$

Question 5

Suppose you invest $$500 at an annual interest rate of 6\% compounded continuously. Which formula gives the amount A$ after t$ years?

Accepted Answer

$$A = 500e$$^{0.06t}$$

Question 6

If $$\log_2$(x) + \log_2$(x-3) = 3$$, what is the value of $$x$$?

Accepted Answer

$$x = 8$$

Question 7

Which of the following is the expanded form of $$\log \left( \sqrt{\dfrac{y^3$}{x^2$ z^5$}} \right)$$?

Accepted Answer

$$\dfrac{3}{2} \log y - \log x^2$ - \dfrac{5}{2} \log z$$

Question 8

A radioactive substance decays according to $$A(t) = A_0$ e$$^{-kt}$$. If the half-life is 1000 years, what is the value of k$?

Accepted Answer

$$k = \dfrac{\ln 2}{1000}$$

Question 9

Which of the following is the correct equation for the vertical asymptote of $$f(x) = \dfrac{x+2}{x^2$-4}$$?

Accepted Answer

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

Question 10

If $$\log_3$(x) = 4$$, what is the value of $$x$$?

Accepted Answer

$$x = 81$$

Question 11

A population of ants grows continuously at a rate of 5\%. If the initial population is 800, what is the population after 10 days?

Accepted Answer

$$800e^{0.05 	imes 10}$$

Question 12

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

Accepted Answer

$$x = 32$$

Question 13

If $$f(x) = \dfrac{2x^2$ + 3x}{x^2$ - 1}$$, what is the $$y-$$intercept of the function?

Accepted Answer

$$y = 0$$

Question 14

Which of the following is the correct expanded form of $$\log_3$(9x)$$?

Accepted Answer

$$\log_3$ 9 + \log_3$ x$$

Question 15

Suppose you take out a $2000 loan at an annual interest rate of 3.5\% compounded monthly. Which formula gives the amount owed after 18 months?

Accepted Answer

$$2000(1 + \dfrac{0.035}{12}$$)^{18}$$

Question 16

Which of the following is the correct solution for $$e^{2x} = 7$?

Accepted Answer

$$x = \dfrac{1}{2} \ln 7$$

Question 17

If $$f(x) = \dfrac{x^2$ + 2x - 3}{x^2$ - 4}$$, which of the following describes all vertical asymptotes?

Accepted Answer

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

Question 18

Which of the following is the correct solution for $$\log_5$(x^2) = 4$?

Accepted Answer

$$x = \pm 25$$

Question 19

If $$f(x) = \dfrac{2x^2$ + 3x}{x^2$ - 1}$$, what is the equation of the horizontal asymptote?

Accepted Answer

$$y = 2$$

Precalculus Test 3 Review: Polynomial, Rational, Exponential, and Logarithmic Functions

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