Question 1

Given the graph above, what is the value of $$\lim_{x 	o 6^-} f(x)$$?

Accepted Answer

$$\infty$$

Question 2

Which of the following best describes the type of discontinuity at $$x = -3$$ for the function $$f(x)$$ shown in the graph?

Accepted Answer

Infinite (essential) discontinuity

Question 3

What is the value of $$\lim_{x 	o 1} f(x)$$ based on the graph?

Accepted Answer

$$0$$

Question 4

Which of the following $$x-$$values is a point where $$f(x) is $$continuous but not differentiable?

Accepted Answer

$$x = 2$$

Question 5

How many vertical asymptotes does the function $$f(x)$$ have, as shown in the graph?

Accepted Answer

Two

Question 6

Which of the following is a horizontal asymptote for $$f(x) as$$ $$x 	o \infty$$?

Accepted Answer

$$y = 0$$

Question 7

At $$x = 4$$, what is the value of $$\lim_{x 	o 4^+} f(x)$$?

Accepted Answer

$$-\infty$$

Question 8

Which of the following statements is true about the continuity of $$f(x) at$$ $$x = 3$$?

Accepted Answer

$$f(x)$$ has a removable discontinuity at $$x = 3$$

Question 9

If $$f(x) is $$defined as in the graph, which of the following best describes the behavior as $$x 	o -\infty$$?

Accepted Answer

$$f(x)$$ oscillates between finite values

Question 10

Which of the following $$x-$$values is a jump discontinuity for $$f(x)$$?

Accepted Answer

$$x = -5$$

Question 11

Suppose $$f(x)$$ models the temperature (in $$^\circC) of a $$chemical reaction over time $$x (in $$minutes). If the reaction must avoid infinite temperature spikes, at which $$x-$$values should the process be stopped based on the graph?

Accepted Answer

$$x = -3$$ and $$x = 4$$

Question 12

Which of the following best describes the left-hand limit $$\lim_{x 	o -3^-} f(x)$$?

Accepted Answer

$$-\infty$$

Limits, Continuity, and Asymptotes from a Graph

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