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

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

Question 1

Which of the following best describes the graph of $$f(x) = x^2$?

Accepted Answer

A parabola opening upward

Question 2

Given the graph of $$f(x) = |x|$$, which of the following statements is true?

Accepted Answer

The graph is a V-shape with its vertex at $$(0,0)$$

Question 3

If a polynomial function has a zero at $$x = 2$$ with multiplicity 3, what does the graph do at $$x = 2$$?

Accepted Answer

It flattens at the x-axis and crosses

Question 4

Which of the following is the correct end behavior for the function $$f(x) = -x^4$ + 2x^2$ - 1$$?

Accepted Answer

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

Question 5

A rational function $$f(x) = \frac{1}{x-3}$$ has which type of discontinuity at $$x=3$$?

Accepted Answer

Infinite discontinuity (vertical asymptote)

Question 6

Which of the following describes the graph of $$f(x) = x^3$?

Accepted Answer

A cubic curve passing through the origin, increasing on both sides

Question 7

If a polynomial $$f(x)$$ has zeros at $$x = -2$$, $$x = 0$$, and $$x = 3$$, which of the following could be its equation?

Accepted Answer

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

Question 8

Which of the following is the correct domain for the function $$f(x) = \sqrt{x-1}$$?

Accepted Answer

$$x \geq 1$$

Question 9

A polynomial function $$f(x)$$ has a zero at $$x = 1$$ with multiplicity 2. What does the graph do at $$x = 1$$?

Accepted Answer

It touches the x-axis and turns around

Question 10

Which of the following is the correct range for the function $$f(x) = |x|$$?

Accepted Answer

$$[0, \infty)$$

Question 11

Given the graph of $$f(x) = \frac{1}{x}$$, which of the following statements is true?

Accepted Answer

The graph has a horizontal asymptote at $$y=0$$ and a vertical asymptote at $$x=0$$

Question 12

If $$f(x) = x^2$ - 4$$, what are the zeros of the function?

Accepted Answer

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

Question 13

Which of the following best describes the end behavior of $$f(x) = x^5$?

Accepted Answer

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

Question 14

Which of the following is the correct interval notation for the domain of $$f(x) = \frac{1}{x+2}$$?

Accepted Answer

$$(-\infty, -2) \cup (-2, \infty)$$

Question 15

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

Accepted Answer

$$(x+1)^2$$

Question 16

Which of the following is the correct description of the graph of $$f(x) = \sqrt{x}$$?

Accepted Answer

Starts at $$(0,0)$$ and increases slowly to the right

Question 17

If a polynomial function has a zero at $$x = -1$$ with multiplicity 4, what does the graph do at $$x = -1$$?

Accepted Answer

It touches the x-axis and turns around

Question 18

Which of the following is the correct range for the function $$f(x) = x^2$?

Accepted Answer

$$[0, \infty)$$

Question 19

Which of the following is the correct interval notation for the domain of $$f(x) = \frac{1}{x^2$-9}$$?

Accepted Answer

$$(-\infty, -3) \cup (-3, 3) \cup (3, \infty)$$

Exam 2

Study Guide - Practice Questions