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# Functions, Graphs, and Limits

# Functions, Graphs, and Limits: Approachable Quiz

Think you’ve got your head wrapped around

*? Put your knowledge to the test. Good luck — the Stickman is counting on you!***Functions, Graphs, and Limits**Q. Which of the following statements is true for a function

*f*(*x*)?*f*(

*x*) cannot cross its horizontal asymptote(s).

A vertical asymptote can only be drawn at

*x*=*a*if*f*(*a*) is undefined.*f*(

*x*) must approach its horizontal asymptote as

*x*approaches ∞.

A vertical asymptote is drawn at x = a if at least one of is either ∞ or -∞

Q. Find all vertical asymptotes (if any) of the function

*x*= 2 and

*x*= -2

*x*= 0

*x*= 0,

*x*= 2, and

*x*= -2

*f*(

*x*) has no vertical asymptotes

Q. The function has

a hole at

*x*= -10 and a vertical asymptote at*x*= 7a vertical asymptote at

*x*= -10 and a hole at*x*= 7vertical asymptotes at

*x*= -10 and*x*= 7holes at

*x*= -10 and*x*= 7Q. Which statement is true?

Q. The function has

a horizontal asymptote

a slant asymptote

a curvilinear asymptote

none of the above

Q. The function has

a horizontal asymptote at

*x*= 0a horizontal asymptote at

*y*= 0a horizontal asymptote at

*x*= 3a horizontal asymptote at

*y*= 3Q. Which of the following pictures could be a graph of the function

Picture1

Picture2

Picture3

Picture4

Q. Which of the following pictures could be a graph of the function

Picture1

Picture2

Picture3

Picture4

Q.

0

-1

∞

-∞

Q. The function

Which function should we choose for p(x) to ensure that .

*p*(

*x*) = ln

*x*

*p*(

*x*) = 1000

*x*

^{2}+ 4

*x*+ 6

*p*(

*x*) = ln

*x*+

*x*

^{2}

*p*(

*x*) = 2

^{x}