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Functions, Graphs, and Limits

Functions, Graphs, and Limits

Functions, Graphs, and Limits: Approachable Quiz

Think you’ve got your head wrapped around Functions, Graphs, and Limits? Put your knowledge to the test. Good luck — the Stickman is counting on you!
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 = 7

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

vertical asymptotes at x = -10 and x = 7

holes at x = -10 and x = 7

Q. 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 = 0

a horizontal asymptote at y = 0

a horizontal asymptote at x = 3

a horizontal asymptote at y = 3

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


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



Q.



0
-1
-∞
Q. For the function  ,

which function should we choose for p(x) to ensure that ?



p(x) = ln x

p(x) = 1000x2 + 4x + 6

p(x) = ln x + x2

p(x) = 2x