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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