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

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

Question 1

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

Accepted Answer

A graph that passes through the origin and opens upward.

Question 2

Given the graph of $$f(x) = x^3$, which of the following statements is true about its symmetry?

Accepted Answer

It is symmetric about the origin.

Question 3

Which graph represents the function $$f(x) = \sqrt{x}$$?

Accepted Answer

A curve starting at $$(0,0)$$ and increasing only in the first quadrant.

Question 4

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

Accepted Answer

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

Question 5

If $$f(x) = x^2$ and g(x$$) = $$x^3$$, which function grows faster as $$x$$ increases?

Accepted Answer

$$g(x)$$ grows faster than $$f(x).$$

Question 6

Which function is not defined for negative values of $$x$$?

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

Which function has a domain of all real numbers except $$x=0$$?

Accepted Answer

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

Question 9

Which graph shows a function that is even?

Accepted Answer

A graph symmetric about the y-axis.

Question 10

Which function has a range of all real numbers?

Accepted Answer

$$f(x) = x^3$

Question 11

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$

Question 12

Which function has a graph that passes through the origin and increases more rapidly for large positive $$x$$ than for large negative $$x$$?

Accepted Answer

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

Question 13

Which function has a graph with two branches, one in the first quadrant and one in the third quadrant, both approaching the axes but never touching them?

Accepted Answer

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

Question 14

Which function is not continuous at $$x=0$$?

Accepted Answer

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

Question 15

Which function has a minimum at $$x=0$$?

Accepted Answer

$$f(x) = x^2$

Question 16

Which function is undefined for $$x\u003c0$$?

Accepted Answer

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

Question 17

Which function has a graph that is always above the x-axis for $$x\u003e0$$?

Accepted Answer

$$f(x) = x^2$

Question 18

Which function has a graph that is a straight line through the origin?

Accepted Answer

$$f(x) = x$$

Question 19

Which function has a graph that is symmetric about the y-axis and has its vertex at the origin?

Accepted Answer

$$f(x) = x^2$

Question 20

Which function has a graph that approaches zero as $$x$$ approaches infinity?

Accepted Answer

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

Parent Functions and Their Graphs: A Precalculus Study Guide

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