Question 1

Which of the following statements about the function $$f(x) = \frac{1}{x} is $$true?

Accepted Answer

It is an odd function because $$f(-x) = -f(x)$$ for all $$x in $$its domain.

Question 2

Given the polynomial $$p(x) = 2x^2$ + x - 3$$, which of the following is a correct factorization?

Accepted Answer

$$p(x) = (2x - 3)(x + 1)$$

Question 3

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

Accepted Answer

$$(-\infty, 9]$$

Question 4

Suppose $$f(x) = 2(x + 3)^2$ - 8. $$What is the vertex of the parabola?

Accepted Answer

$$(-3, -8)$$

Question 5

Given the rational function $$r(x) = \frac{3x}{x-4}$$, what is the equation of its vertical asymptote?

Accepted Answer

$$x = 4$$

Question 6

Which of the following functions is neither even nor odd?

Accepted Answer

$$h(x) = x^2$ + x$$

Question 7

If $$f(x) = x^4$ - 5x^2$ + 4 = 0$$, which of the following is NOT a solution?

Accepted Answer

$$x = 3$$

Question 8

A rational function $$f(x) = \frac{x^2$ - 5x - 3}{x^2$ + x - 12}$$ has a hole at which $$x-$$value?

Accepted Answer

$$x = 4$$

Question 9

Given $$f(x) = x^3$ - 2x^2$ - x + 2$$, which of the following is a root of $$f(x)$$?

Accepted Answer

$$x = 2$$

Question 10

Which of the following best describes the end behavior of $$f(x) = -2x^3$ + 3x^2$ - 4 as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o -\infty$$

Question 11

If $$f(x) = x^2$ - 4$$ and $$g(x) = x - 2$$, what is $$\frac{f(x)}{g(x)}$$ simplified?

Accepted Answer

$$x + 2$$

Question 12

Which of the following is the correct solution set for $$f(x) = 0$$ where $$f(x) = \frac{1}{2}x^2$ - 8$$?

Accepted Answer

$$x = \pm 4\sqrt{2}$$

Question 13

Which of the following statements about rational functions is TRUE?

Accepted Answer

A rational function can have a hole where the numerator and denominator share a common factor.

Question 14

Given $$f(x) = x^2$ + 2x + 1$$, which of the following describes its graph?

Accepted Answer

A parabola opening up with vertex at $$(-1, 0)$$

Question 15

If $$f(x) = x^3$ - 3x^2$ + 4$$, what is the $$y-$$intercept of the graph?

Accepted Answer

$$y = 4$$

Question 16

Which of the following is the correct range for $$f(x) = \sqrt{x + 2}$$?

Accepted Answer

$$[0, \infty)$$

Question 17

If $$f(x) = x^2$ - 4x + 3$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 18

Which of the following best describes the symmetry of $$g(x) = |x| + x^2$?

Accepted Answer

Neither

Question 19

If $$f(x) = x^3$ + 2x^2$ - x - 2$$ and $$x = -2 is a $$root, which theorem justifies this?

Accepted Answer

Factor Theorem

Question 20

Given the polynomial $$f(x) = x^4$ - 5x^2$ + 4$$, what is the sum of all real roots?

Accepted Answer

$$0$$

Question 21

A polynomial function $$f(x)$$ has roots at $$x = 2$$ and $$x = -2. $$Which of the following could be $$f(x)$$?

Accepted Answer

$$f(x) = x^2$ - 4$$

College Algebra Study Guide: Functions, Polynomials, Rational Functions, and Graphs

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