Quiz about Unit 4C - All Characteristics of Rational Functions

Question 1

What type of rational function is this and what is the equation of the horizontal asymptote?

$$f\left(x\right)=\frac{-2x^2-2x}{x^2-3x-4}$$

Accepted Answer

PEy = -2

Answer

BHy = 0

Answer

PEy = 2

Answer

TH

There isn't one

Question 2

What is the equation of the vertical asymptote?

Accepted Answer

x = 1

Answer

y = 1

Answer

(2, 4)

Answer

There isn't one.

Question 3

Which of the following is the correct domain restriction?

Accepted Answer

$$x e1,\ 2$$

Answer

$$x
e1$$

Answer

$$x
e2$$

Answer

There aren't any.

Question 4

Find the x-intercept(s) of the rational function.

Accepted Answer

x-int: $$\left(-2,\ 0\right)$$

Answer

x-int: $$\left(0,\ -2\right)$$

Answer

x-int: $$\left(2,\ 0\right)$$

Answer

x-int: $$\left(-2,\ 0\right)\ \&\ \left(2,\ 4\right)$$

Question 5

Find the y-intercept(s) of the rational function.

Accepted Answer

y-int: $$\left(0,\ -2\right)$$

Answer

y-int: $$\left(-2,\ 0\right)$$

Answer

y-int: $$\left(0,\ -2\right)\ \&\ \left(2,\ 4\right)$$

Answer

y-int: $$\left(0,\ -2\right)\ \&\ \left(0,\ 1\right)$$

Question 6

Find the x-intercept(s), if one exists.

$$f\left(x\right)=\frac{\left(x+1\right)\left(x-1\right)}{x\left(x+1\right)}$$

Accepted Answer

(1, 0)

Answer

(-1, 0)

Answer

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

Answer

(0, 0), (1, 0)

Question 7

Find the vertical asymptote(s), if one exists.

$$f\left(x\right)=\frac{\left(x+1\right)\left(x-1\right)}{x\left(x+1\right)}$$

Accepted Answer

x = 0

Answer

(0, 0)

Answer

(-1, 0)

Answer

y = 0

Question 8

What are the coordinates of the y-intercept, if one exists.

Accepted Answer

there isn't one

Answer

(0, 0)

Answer

(0, 1)

Answer

(0, -1)

Question 9

What are the coordinates of the y-intercept, if one exists?

Accepted Answer

(0, 1)

Answer

(0, 0)

Answer

(0, -1)

Answer

(1, 0)

Question 10

What is the equation of the vertical asymptote?

$$f\left(x\right)=\frac{4x^2+8x}{x+3}$$

Accepted Answer

x = -3

Answer

x = 3

Answer

x = 0

Answer

x = -2

Question 11

What are the coordinates of the y-intercept, if one exists?

Accepted Answer

(0, -4)

Answer

(0, 4)

Answer

(0, 0)

Answer

(0, 1)

Question 12

What type of function is shown?

Accepted Answer

bottom heavy

Answer

top heavy

Answer

powers equal

Question 13

What is the equation of the vertical asymptote?

Accepted Answer

$$x=2$$

Answer

$$x=0$$

Answer

$$y=0$$

Answer

$$y=2$$

Question 14

What type of function is graphed?

Accepted Answer

powers equal

Answer

bottom heavy

Answer

top heavy

Question 15

Determine the domain restriction.

Accepted Answer

$$x e-3,\ 2$$

Answer

$$x e-3,\ 1,\ 2$$

Answer

$$x e-3,\ 1$$

Answer

$$x
e2$$

Question 16

What type of function is graphed?

Accepted Answer

top heavy

Answer

bottom heavy

Answer

powers equal

Question 17

What is the equation of the slant asymptote?

Accepted Answer

$$y=x-2$$

Answer

$$y=-x+2$$

Answer

$$y=x+2$$

Answer

$$y=-x-2$$

Question 18

Find the y-intercept.

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

Accepted Answer

(0, -2)

Answer

(0, 2)

Answer

(0, 4)

Answer

it is undefined

Question 19

Find the x-intercept.

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

Accepted Answer

(4, 0)

Answer

(0, -2)

Answer

(-4, 0)

Answer

(0 -4)

Question 20

What are the asymptotes?

Accepted Answer

x = -3        y = 1

Answer

x = 3         y = 1

Answer

x = -3        y = -1

Answer

x = 3         y = -1

Question 21

Select Which functions have a horizontal asymptote of $$y=3$$ ? SELECT ALL THAT APPLY.

Accepted Answer

$$f\left(x\right)=\frac{3x^2}{x^2-9}$$

Accepted Answer

$$f\left(x\right)=\frac{6\left(x+5\right)}{2x}$$

Answer

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

Answer

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

Answer

$$f\left(x\right)=\frac{x^2+x-2}{x^3}$$

Unit 4C - All Characteristics of Rational Functions

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