1.8 Practice (select problems)

1.8 Rational Functions and Zeros
HW: PRACTICE #1-13
Select Problems**

Multiple Choice

How do you find Zeros of a Rational Function?

• Non-Removable

  Factors in the Numerator

• Non-Removable

  Factors in the Denominator

• Removable

  Factors in the Numerator

• Removable

  Factors in the

  Denominator

• Plug in

  x=0

Math Response

1. Factor f(x)

Type answer here

Correct Answer: \frac{x-1}{\left(x-3\right)\left(x+3\right)}

Deg^°

Rad

Multiple Choice

1. Find the Zeros of f(x)

• x=1

• x=9

• x=-1

• x=3

• x=-3

Multiple Choice

2. Find the Zeros of d(t).

• t=-3

• t=1

• t=3

• t=4

• No Zeros

​Find the Zeros of the Function

Math Response

5. What is the Zero of f(x).

   (type the x value only as your answer)

Type answer here

Correct Answer: 5

Deg^°

Rad

Math Response

6. Factor the function, c(n)

   (type factored function)

Type answer here

Correct Answer: \frac{n\left(n+5\right)}{\left(n+5\right)\left(n-5\right)}

Deg^°

Rad

Multiple Choice

6. What are the Zeros of c(n) ?

• n=5

• n=-5

• n=0

• n=1

• No Zeros

Math Response

9. Factor g(x), completely

   (type factored function)

Type answer here

Correct Answer: \frac{4\left(x+5\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}

Deg^°

Rad

Multiple Choice

a. What is the Domain?

• $$x\ne5$$

  $$x\ne4$$

• $$x\ne2$$

  $$x\ne-2$$

• $$x\ne-5$$

  $$x\ne2$$

• $$x\ne-4$$

  $$x\ne4$$

• All Real

  Numbers

Multiple Choice

How do you find Holes of a Rational Function?

• Non-Removable

  Factors in the Numerator

• Non-Removable

  Factors in the Denominator

• Removable

  Factors in the

  Denominator

  and Numerator

• Plug in

  x=0

Multiple Choice

b. What is the x-value of the Hole of g(x)?

• x=-5

• x=2

• x=-2

• x=0

• No Holes

Multiple Choice

c. What is the Zero of g(x)?

• x = 0
• x = -5

• x = 2

• x = -1
• No Zeros

Multiple Choice

How do you find Vertical Asymptotes of a Rational Function?

• Non-Removable

  Factors in the Numerator

• Non-Removable

  Factors in the Denominator

• Removable

  Factors in the Numerator

• Removable

  Factors in the

  Denominator

• Plug in

  x=0

Multiple Choice

d. What is the Vertical Asymptote of g(x)?

• x=-2

• x=5

• x=2

• x=0

• No Vertical

  Asymptote

Multiple Choice

How do you find Horizontal Asymptotes?

• Plug in x=0

• Take limit

  to infinity

• factor the function

• Set Denominator

  equal to zero

Multiple Choice

e. What is the Horizontal Asymptote of g(x)?

• y=0

• y=-5

• y=4

• y=1

• No Horizontal

  Asymptote

Multiple Choice

How do you find the y-intercept of a Rational Function?

• Non-Removable

  Factors in the Numerator

• Non-Removable

  Factors in the Denominator

• Removable

  Factors in the Numerator

• Removable

  Factors in the

  Denominator

• Plug in

  x=0

Multiple Choice

f. What is the y-intercept of g(x)?

• $$\left(0,\ 10\right)$$

• $$\left(0,\ 4\right)$$

• $$\left(10,\ 0\right)$$

• $$\left(0,\ 40\right)$$

• No y-intercept

​Complete the Rest of the Practice Problems for 1.8 Practice.

Match

What does each sign say about the function?

• Positive

• Negative

• Zero

• Undefined

Above the

x-axis

Below the

x-axis

x-intercept

Hole

or V. Asymptote

• Above the

  x-axis

• Below the

  x-axis

• x-intercept

• Hole

  or V. Asymptote

Multiple Choice

13. What is the Sign on the interval?

    $$-\infty<x<-5$$

• Positive

• Negative

• Undefined

• Zero

Multiple Choice

13. What is the Sign on the interval?

    $$x=-5$$

• Positive

• Negative

• Undefined

• Zero

Multiple Choice

13. What is the Sign on the interval?

    $$-5<x<-2$$

• Positive

• Negative

• Undefined

• Zero

Multiple Choice

13. What is the Sign on the interval?

    $$x=-2$$

• Positive

• Negative

• Undefined

• Zero

Multiple Choice

13. What is the Sign on the interval?

    $$-2<x<2$$

• Positive

• Negative

• Undefined

• Zero

Multiple Choice

13. What is the Sign on the interval?

    $$x=2$$

• Positive

• Negative

• Undefined

• Zero

Multiple Choice

13. What is the Sign on the interval?

    $$2<x<\infty$$

• Positive

• Negative

• Undefined

• Zero