Let's review asymptotes!

Vertical Asymptotes

Horizontal Asymptotes

Mixed

Domain

Surprise for you

100

What is a vertical asymptote ?

A vertical asymptote is when the denominator equals zero. You can factor and solve the denominator to find the asymptote.

100

What is a horizontal asymptote and what are three ways using the degrees you can tell what the horizontal asymptote is?

Horizontal line that the function never touches.

Numerator exponent is bigger= then it is none Numerator exponent is smaller=then it is 0

Exponents are the same= divide coefficients

100

Find the VA, HA of f(x)=x^2+2x/-4x+8

x(x+2)/-4(x-2)

VA= 2 HA= None

100

The domain of a rational function consists of all real numbers except _________.

Discontinuities (Asymptotes, holes)

100

The domain for the function:

f(x)=4x^3-10x^2-8x+7

All real numbers

200

Find the vertical asymptote. y= x^2+2x-3/x^2-5x-6

(x+3)(x-1)/(x+1)(x-5) VA= x=-1 and x=5

200

Find the horizontal asymptote. y= x+4/x^2+6x+8

HA= 0

200

Find the VA, and HA. f(x)=x^3-16x/-4x^2+4x+24

VA= x=3, x=-2 HA= None

200

Write the domain of the function:

f(x)=(x+1)/((x+2)(x-7)

(-oo,-2)(-2,7)(7,oo)

200

The domain for the function:

R(x)=sqrt(x+5)

[-5,oo)

300

Find the vertical asymptote. y= x^2+2x-3/x^2-5x-6

(x+3)(x-1)/(x+1)(x-5) VA= x=-1 and x=5

300

Find the horizontal asymptote. y=3x^3+10/2x^2-16

HA= None

300

factor x²+5x+6

(x+2)(x+3)

300

Find the domain:

f(x)=(x+2)/(x^2+2x-15

(-oo,-5)(-5,3)(3,oo)

300

The domain for the function:

R(x)=(x-2)/(x^2-25)

All real numbers except 5 and -5

400

Find the vertical asymptote. y= x^3-8/x^2+5x+6

VA= x=-2, x=-3

400

Find the horizontal asymptote. y=3x^2+x-6/x^2+8x+15

HA= 3

400

Vertical asymptote(s) of

(x²+3)/(x²+3x-4)

x=1 x=-4

400

Find the domain:

(x^2-1)/(x^2-2x-3

(-oo,3)(3,oo)

400

Zeros of the function (x²-2x-3)/(x+3)

x=-1,3

500

Find the vertical asymptote. y= x^3-4x^2+4x/x^2-16

x(x^2-4x+4)/(x+4)(x-4) x(x-2)(x-2)/(x+4)(x-4) VA= x=0, x=2

500

Find the horizontal asymptote. y= 3x^4-5x^2+4/2x^4-2x^3+5

HA= 3/2

500

add/subtract the polynomials

(2x²+3x+7)-(x²+4)

x²+3x+3

500

Find the domain:

f(x)=√x²+5x+6

(-oo,3][-2,oo)

500

Zeros of the function (x²-x-20)/(x-5)

x=-4