Q: Which of the following best describes the end behavior of the function $y = x^2 - 4x + 3$?

As $x \to \infty$, $y \to \infty$; as $x \to -\infty$, $y \to \infty$

Question 1

Which of the following best describes the end behavior of the function $y = x^2 - 4x + 3$?

Accepted Answer

As $x 	o \infty$, $y 	o \infty$; as $x 	o -\infty$, $y 	o \infty$

Question 2

For the function $y = x^3 - 3x + 3$, which of the following is a critical point?

Accepted Answer

$(1, 1)$

Question 3

What is the domain of the function $y = \frac{x^2}{x^2 + 9}$?

Accepted Answer

$(-\infty, \infty)$

Question 4

Which function has a vertical asymptote at $x = 2$?

Accepted Answer

$y = \frac{x + 1}{x - 2}$

Question 5

Find the $y$-intercept of the function $y = x^4 - 2x^2$.

Accepted Answer

$(0, 0)$

Question 6

Which of the following statements about $y = \frac{x^2}{x^2 + 9}$ is true?

Accepted Answer

It has a horizontal asymptote at $y = 1$

Question 7

For the function $y = x^4 - 2x^2$, what are the $x$-intercepts?

Accepted Answer

$(0, 0), (\sqrt{2}, 0), (-\sqrt{2}, 0)$

Question 8

Which function has no critical points?

Accepted Answer

$y = \frac{x + 1}{x - 2}$

Question 9

A pharmaceutical company models the concentration of a drug in the bloodstream by $y = \frac{x^2}{x^2 + 9}$, where $x$ is time in hours. What is the maximum possible concentration as $x$ increases indefinitely?

Accepted Answer

$y = 1$

Question 10

For the function $y = x^2 - 4x + 3$, what is the critical point and its value?

Accepted Answer

$(2, -1)$

Question 11

Which of the following describes the intervals of increase and decrease for $y = \frac{x^2}{x^2 + 9}$?

Accepted Answer

Increasing on $(0, \infty)$; decreasing on $(-\infty, 0)$

Question 12

A chemical reaction rate is modeled by $y = \frac{x + 1}{x - 2}$. What is the horizontal asymptote of this function?

Accepted Answer

$y = 1$

Question 13

Which function has a $y$-intercept at $(0, 3)$?

Accepted Answer

$y = x^2 - 4x + 3$

Question 14

For $y = x^3 - 3x + 3$, what is the value of $y$ at the critical point $x = -1$?

Accepted Answer

$y = 5$

Question 15

Which of the following functions has both a vertical and a horizontal asymptote?

Accepted Answer

$y = \frac{x + 1}{x - 2}$

Question 16

A medical researcher is analyzing the function $y = x^4 - 2x^2$ to model the spread of a disease. What are the critical points of this function?

Accepted Answer

$(0, 0), (1, -1), (-1, -1)$

Question 17

For the function $y = \frac{x + 1}{x - 2}$, what is the $y$-intercept?

Accepted Answer

$(0, -\frac{1}{2})$

Question 18

Which function has a critical point at $(0, 0)$ and a horizontal asymptote at $y = 1$?

Accepted Answer

$y = \frac{x^2}{x^2 + 9}$

Question 19

A population model is given by $y = x^4 - 2x^2$. What is the behavior of the function as $x 	o \infty$?

Accepted Answer

$y 	o \infty$

Graphing Functions: 4.4

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