Question 1

Given the graph of $$g(x)$$ above, what is $$\displaystyle \lim_{x 	o -1^-} g(x)$$?

Accepted Answer

$$-2$$

Question 2

Given the graph of $$g(x)$$ above, what is $$g(-1)$$?

Accepted Answer

$$0$$

Question 3

Based on the graph of $$g(x)$$, which of the following statements is true about the continuity of $$g(x) at$$ $$x = 0$$?

Accepted Answer

$$g(x) is $$not continuous at $$x = 0$$ because \displaystyle \lim_{x 	o 0} g(x)$ does not exist.

Question 4

From the graph of $$g(x)$$, what is $$\displaystyle \lim_{x 	o 2^+} g(x)$$?

Accepted Answer

$$-1$$

Question 5

According to the graph, is $$x = 1 in $$the domain of $$g(x)$$? Why or why not?

Accepted Answer

No, because there is an open circle at $$x = 1.$$

Question 6

What is $$\displaystyle \lim_{x 	o -2} g(x)$$ based on the graph?

Accepted Answer

$$2$$

Question 7

Which of the following best describes the discontinuity at $$x = -2$$ for $$g(x)$$?

Accepted Answer

Jump discontinuity

Question 8

For which value of $$c$$ does $$g(x)$$ have a removable discontinuity based on the graph?

Accepted Answer

$$c = -1$$

Question 9

What is $$g(2)$$ according to the graph?

Accepted Answer

$$1$$

Question 10

Which of the following is true about $$\displaystyle \lim_{x 	o 1} g(x)$$?

Accepted Answer

The limit does not exist because the left and right limits are not equal.

Analyzing Limits and Continuity from a Graph

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