Q: If $$f(x)$$ has a vertical asymptote at $$x = 3$$, which of the following is true?

$$\lim\limits_{x \to 3^-} f(x) or$$ $$\lim\limits_{x \to 3^+} f(x) is $$infinite

Question 1

Given the graph of $$f(x)$$ shown, what is $$\lim\limits_{x 	o 3^-} f(x)$$?

Accepted Answer

$$\infty$$

Question 2

Given the graph of $$f(x)$$, what is $$\lim\limits_{x 	o 3^+} f(x)$$?

Accepted Answer

$$-\infty$$

Question 3

Given the graph of $$f(x)$$, what is $$\lim\limits_{x 	o 3} f(x)$$?

Accepted Answer

DNE (Does Not Exist)

Question 4

Given the graph of $$f(x)$$, what is $$\lim\limits_{x 	o -2^-} f(x)$$?

Accepted Answer

$$\infty$$

Question 5

Given the graph of $$f(x)$$, what is $$\lim\limits_{x 	o -2^+} f(x)$$?

Accepted Answer

$$\infty$$

Question 6

Given the graph of $$f(x)$$, what is $$\lim\limits_{x 	o -2} f(x)$$?

Accepted Answer

$$\infty$$

Question 7

Given the graph of $$f(x)$$, what is $$\lim\limits_{x 	o -\infty} f(x)$$?

Accepted Answer

$$0$$

Question 8

Given the graph of $$f(x)$$, what is $$\lim\limits_{x 	o \infty} f(x)$$?

Accepted Answer

$$1$$

Question 9

Which of the following statements best describes the behavior of $$f(x) as$$ $$x$$ approaches $$3$$ from the left?

Accepted Answer

$$f(x)$$ increases without bound

Question 10

If $$f(x)$$ models the concentration of a chemical in a reaction over time $$x$$, and $$\lim\limits_{x 	o \infty} f(x) = 1$$, what does this imply about the long-term behavior of the reaction?

Accepted Answer

The concentration approaches a steady-state value of $$1$$

Question 11

Suppose $$f(x)$$ represents the temperature of a cooling object over time $$x$$, and $$\lim\limits_{x 	o -\infty} f(x) = 0. $$What does this mean in practical terms?

Accepted Answer

As time goes far into the past, the temperature approaches $$0$$

Question 12

If $$f(x)$$ has a vertical asymptote at $$x = 3$$, which of the following is true?

Accepted Answer

$$\lim\limits_{x 	o 3^-} f(x) or$$ $$\lim\limits_{x 	o 3^+} f(x) is $$infinite

Guided Practice: Infinite Limits and Limits at Infinity Using Graphs

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