$$f(x) \to -\infty as$$ $$x \to \infty$$ and $$f(x) \to -\infty as$$ $$x \to -\infty$$

$$f(x) \to \infty as$$ $$x \to \infty$$ and $$f(x) \to -\infty as$$ $$x \to -\infty$$

Question 1

Which of the following graphs represents the function $$f(x) = x^2$?

Accepted Answer

A graph that passes through the origin and opens upward, forming a parabola symmetric about the y-axis.

Question 2

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

Accepted Answer

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

Question 3

Which of the following graphs represents the function $$f(x) = x^3$?

Accepted Answer

A graph that passes through the origin, is symmetric about the origin, and increases to the right and decreases to the left.

Question 4

Which of the following best describes the domain and range of the function $$f(x) = \sqrt{x}$$?

Accepted Answer

Domain: $$[0, \infty)$$, Range: $$[0, \infty)$$

Question 5

Which of the following graphs represents the function $$f(x) = \frac{1}{x}$$?

Accepted Answer

A graph with two branches, one in the first quadrant and one in the third quadrant, both approaching the axes but never touching them.

Question 6

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

Accepted Answer

$$[0, \infty)$$

Question 7

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$

Question 8

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$

Question 9

Which of the following best describes the domain of the function $$f(x) = \frac{1}{x}$$?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 10

Which of the following graphs represents the function $$f(x) = |x|$$?

Accepted Answer

A graph that forms a 'V' shape with its vertex at the origin, opening upward.

Question 11

Which of the following best describes the range of the function $$f(x) = |x|$$?

Accepted Answer

$$[0, \infty)$$

Question 12

Which of the following functions has a vertical asymptote at $$x = 0$$?

Accepted Answer

$$f(x) = \frac{1}{x}$$

Question 13

Which of the following functions is neither even nor odd?

Accepted Answer

$$f(x) = \sqrt{x}$$

Question 14

Which of the following best describes the end behavior of the function $$f(x) = x^3$?

Accepted Answer

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

Question 15

Which of the following functions is not defined for negative values of $$x$$?

Accepted Answer

$$f(x) = \sqrt{x}$$

Question 16

Which of the following best describes the symmetry of the function $$f(x) = |x|$$?

Accepted Answer

Even symmetry (symmetric about the y-axis)

Question 17

Which of the following functions has a horizontal asymptote at $$y = 0$$?

Accepted Answer

$$f(x) = \frac{1}{x}$$

Question 18

Which of the following best describes the domain of the function $$f(x) = |x|$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 19

Which of the following functions is defined for all real numbers except $$x = 0$$?

Accepted Answer

$$f(x) = \frac{1}{x}$$

Question 20

Which of the following best describes the range of the function $$f(x) = \frac{1}{x}$$?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Parent Functions and Their Graphs: A Precalculus Study Guide

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