As $x \to 2^+$, $f(x) \to +\infty$

Question 1

Which of the following is the correct equation for a rational function with a vertical asymptote at $x = -2$ and a horizontal asymptote at $y = 3$?

Accepted Answer

$f(x) = \frac{1}{x+2} + 3$

Question 2

Given the function $f(x) = \frac{1}{x}$, what happens to $f(x)$ as $x$ approaches $0$ from the positive side?

Accepted Answer

$f(x)$ approaches $+\infty$

Question 3

What is the domain of the function $f(x) = \frac{1}{x-4}$?

Accepted Answer

$(-\infty, 4) \cup (4, \infty)$

Question 4

Which of the following describes the transformation from $f(x) = \frac{1}{x}$ to $g(x) = \frac{1}{x-2} + 1$?

Accepted Answer

Shift right 2 units and up 1 unit

Question 5

For the function $f(x) = \frac{1}{x-3}$, what is the equation of the vertical asymptote?

Accepted Answer

$x = 3$

Question 6

Given $f(x) = \frac{1}{x+1}$, what is $\lim\limits_{x 	o -1^+} f(x)$?

Accepted Answer

$+\infty$

Question 7

If $f(x) = \frac{1}{x-2}$, what is the range of $f(x)$?

Accepted Answer

$(-\infty, 0) \cup (0, \infty)$

Question 8

Which of the following best describes the end behavior of $f(x) = \frac{1}{x}$ as $x 	o \infty$?

Accepted Answer

$f(x) 	o 0$

Question 9

For the function $f(x) = \frac{1}{(x-2)^2}$, what happens to $f(x)$ as $x$ approaches $2$?

Accepted Answer

$f(x)$ approaches $+\infty$ from both sides

Question 10

Given the graph of $f(x) = \frac{1}{x-1} + 2$, what is the equation of the horizontal asymptote?

Accepted Answer

$y = 2$

Question 11

Suppose $f(x) = \frac{1}{x-3} + 2$. What is $\lim\limits_{x 	o 3^-} f(x)$?

Accepted Answer

$-\infty$

Question 12

Which of the following functions has a vertical asymptote at $x = -4$ and a horizontal asymptote at $y = -2$?

Accepted Answer

$f(x) = \frac{1}{x+4} - 2$

Question 13

If $f(x) = \frac{1}{x-2}$, which of the following statements is true?

Accepted Answer

As $x 	o 2^+$, $f(x) 	o +\infty$

Question 14

Given $f(x) = \frac{1}{x-1}$, what is the value of $\lim\limits_{x 	o 1} f(x)$?

Accepted Answer

The limit does not exist

Question 15

Which of the following best describes the domain of $f(x) = \frac{1}{x-2} + 3$?

Accepted Answer

$(-\infty, 2) \cup (2, \infty)$

Question 16

For the function $f(x) = \frac{1}{x-2}$, what is the value of $\lim\limits_{x 	o 2^-} f(x)$?

Accepted Answer

$-\infty$

Question 17

Which of the following is the correct arrow notation for $f(x) = \frac{1}{x}$ as $x 	o 0^-$?

Accepted Answer

$f(x) 	o -\infty$

Question 18

A rational function has a vertical asymptote at $x = 5$ and a horizontal asymptote at $y = -1$. Which of the following could be its equation?

Accepted Answer

$f(x) = \frac{1}{x-5} - 1$

Question 19

Given $f(x) = \frac{1}{(x-2)^2}$, what is the range of $f(x)$?

Accepted Answer

$(0, \infty)$

Question 20

Suppose $f(x) = \frac{1}{x-2} + 3$. What is $\lim\limits_{x 	o \infty} f(x)$?

Accepted Answer

$3$

E2,E3

Study Guide - Practice Questions