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 -∞
![](https://media1.shmoop.com/images/calculus/cal_fnlim_quiz_2_latek_1.png)
Q. Find all vertical asymptotes (if any) of the function
![](https://media1.shmoop.com/images/calculus/cal_fnlim_quiz_2_latek_2.png)
x = 2 and x = -2
x = 0
x = 0, x = 2, and x = -2
f(x) has no vertical asymptotes
Q. The function
has
![](https://media1.shmoop.com/images/calculus/cal_fnlim_quiz_2_latek_3.png)
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?
![](https://media1.shmoop.com/images/calculus/cal_fnlim_quiz_2_latek_4.png)
![](https://media1.shmoop.com/images/calculus/cal_fnlim_quiz_2_latek_5.png)
![](https://media1.shmoop.com/images/calculus/cal_fnlim_quiz_2_latek_6.png)
![](https://media1.shmoop.com/images/calculus/cal_fnlim_quiz_2_latek_7.png)
Q. The function
has
![](https://media1.shmoop.com/images/calculus/cal_fnlim_quiz_2_latek_8.png)
a horizontal asymptote
a slant asymptote
a curvilinear asymptote
none of the above
Q. The function
has
![](https://media1.shmoop.com/images/calculus/cal_fnlim_quiz_2_latek_9.png)
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
?
![](https://media1.shmoop.com/images/calculus/cal_fnlim_quiz_2_latek_10.png)
![](https://media1.shmoop.com/images/calculus/cal_fnlim_quiz_2_graphik_9.png)
![](https://media1.shmoop.com/images/calculus/cal_fnlim_quiz_2_graphik_11.png)
![](https://media1.shmoop.com/images/calculus/cal_fnlim_quiz_2_graphik_12.png)
![](https://media1.shmoop.com/images/calculus/cal_fnlim_quiz_2_graphik_12.png)
Q. Which of the following pictures could be a graph of the function
![](https://media1.shmoop.com/images/calculus/cal_fnlim_quiz_2_graphik_13.png)
![](https://media1.shmoop.com/images/calculus/cal_fnlim_quiz_2_graphik_14.png)
![](https://media1.shmoop.com/images/calculus/cal_fnlim_quiz_2_graphik_15.png)
![](https://media1.shmoop.com/images/calculus/cal_fnlim_quiz_2_graphik_16.png)
Q.
![](https://media1.shmoop.com/images/calculus/cal_fnlim_quiz_2_latek_12.png)
0
-1
∞
-∞
Q. For the function
,
![](https://media1.shmoop.com/images/calculus/cal_fnlim_quiz_2_latek_13.png)
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