Q: Given $$f(x) = \frac{2x^2$ - 8}{x^2$ - 4}$$, what is $$f(x) in $$lowest terms?

$$f(x) = 2$$,\ x \neq 2,\ x \neq -2$

Q: Which of the following is the correct definition of an exponential function?

$$f(x) = ca^x$$,\ where\ c \u003e 0,\ a \u003e 0,\ a \neq 1$

Question 1

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

Accepted Answer

$$f(x) = a_n x^n + a_{n-1} x$$^{n-1}$$ + \ldots + a_1$ x + a_0$,\ where\ a_i\ are\ real\ numbers\ and\ n\ is\ a\ non	ext{-}negative\ integer$

Question 2

Given the polynomial $$f(x) = x^4$ - 5x^2$ + 4$$, which of the following is a correct list of all real zeros?

Accepted Answer

$$x = -2,\ x = -1,\ x = 1,\ x = 2$$

Question 3

Which of the following statements about the graph of a polynomial function is TRUE?

Accepted Answer

The graph of a polynomial function is always continuous and smooth.

Question 4

If $$f(x) = x^3$ - 4x^2$ + 5x - 2$$, use the Rational Zero Theorem to determine which of the following is a possible rational zero.

Accepted Answer

$$x = 2$$

Question 5

Let $$z = 2 + 3i$$ and $$w = 1 - 2i. $$What is $$z \cdot w$$?

Accepted Answer

$$8 - i$$

Question 6

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

Accepted Answer

$$f(x) = \frac{p(x)}{q(x)}$$,\ where\ p(x)\ and\ q(x)\ are\ polynomials\ and\ q(x) 
eq 0$

Question 7

Given $$f(x) = \frac{2x^2$ - 8}{x^2$ - 4}$$, what is $$f(x) in $$lowest terms?

Accepted Answer

$$f(x) = 2$$,\ x 
eq 2,\ x 
eq -2$

Question 8

Find the vertical asymptote(s) of the rational function $$f(x) = \frac{x+1}{x^2$ - 4}.$$

Accepted Answer

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

Question 9

If a zero of a polynomial has even multiplicity, what does the graph do at that zero?

Accepted Answer

It touches the x-axis and turns around.

Question 10

Solve the inequality $$x^2 - 5x + 6$$ \u003c 0$$.

Accepted Answer

$$2 \u003c x \u003c 3$$

Question 11

Given $$f(x) = x^2$ + 1$$ and $$g(x) = \sqrt{x}$$, what is the domain of the composite function $$f(g(x))$$?

Accepted Answer

$$x \geq 0$$

Question 12

Which of the following functions is one-to-one?

Accepted Answer

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

Question 13

Find the inverse of the function $$f(x) = 3x - 5.$$

Accepted Answer

$$f^{-1}(x$$) = \frac{x+5}{3}$$

Question 14

Which of the following is the correct definition of an exponential function?

Accepted Answer

$$f(x) = ca^x$$,\ where\ c \u003e 0,\ a \u003e 0,\ a 
eq 1$

Question 15

What is the value of $$e ($$Euler's number) to three decimal places?

Accepted Answer

$$2.718$$

Question 16

Convert the logarithmic equation $$\log_2$(x) = 5 to $$its equivalent exponential form.

Accepted Answer

$$x = 2^5$

Question 17

Solve for $$x$$: $$\log_{10}(x) = 3.$$

Accepted Answer

$$x = 1000$$

Question 18

Which property of logarithms allows you to write $$\log(ab) = \log(a) + \log(b)$$?

Accepted Answer

Product property

Question 19

A certain radioactive substance decays according to the model $$A(t) = A_0$ e$$^{-0.03t}$$. If the initial amount is 100$ grams, how much remains after 10$ years? (Round to the nearest gram.)

Accepted Answer

$$74$$ grams

Question 20

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

Accepted Answer

$$y = 2$$

Polynomial, Rational, Exponential, and Logarithmic Functions: Study Guide

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