1.8 Practice (select problems)

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

x=1

x=9

x=-1

x=3

x=-3

t=-3

t=1

t=3

t=4

No Zeros

n=5

n=-5

n=0

n=1

No Zeros

$$x\ne5$$

$$x\ne4$$

$$x\ne2$$

$$x\ne-2$$

$$x\ne-5$$

$$x\ne2$$

$$x\ne-4$$

$$x\ne4$$

All Real

Numbers

Non-Removable

Factors in the Numerator

Non-Removable

Factors in the Denominator

Removable

Factors in the

Denominator

and Numerator

Plug in

x=0

x=-5

x=2

x=-2

x=0

No Holes

x = -5

x = 2

No Zeros

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

x=-2

x=5

x=2

x=0

No Vertical

Asymptote

Plug in x=0

Take limit

to infinity

factor the function

Set Denominator

equal to zero

y=0

y=-5

y=4

y=1

No Horizontal

Asymptote

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

$$\left(0,\ 10\right)$$

$$\left(0,\ 4\right)$$

$$\left(10,\ 0\right)$$

$$\left(0,\ 40\right)$$

No y-intercept

Positive

Negative

Undefined

Zero

Positive

Negative

Undefined

Zero

Positive

Negative

Undefined

Zero

Positive

Negative

Undefined

Zero

Positive

Negative

Undefined

Zero

Positive

Negative

Undefined

Zero

Positive

Negative

Undefined

Zero