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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