Let's review asymptotes!

Vertical Asymptotes

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.

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

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

400

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

VA= x=-2, x=-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

Horizontal Asymptotes

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

200

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

HA= 0

300

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

HA= None

400

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

HA= 3

500

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

HA= 3/2

Mixed

100

Find the VA, HA of  f(x)=x^2+2x/-4x+8

x(x+2)/-4(x-2) 

VA= 2 HA= None  

200

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

VA= x=3, x=-2 HA= None Hole= None Zero= x=-4, x=4, x=0

300

factor x²+5x+6

(x+2)(x+3)

400

Draw the vertical asymptote(s) for

Do this on your paper.

(x²+3)/(x²+3x-4)

x=1 x=-4

500

add/subtract the polynomials

(2x²+3x+7)-(x²+4)

x²+3x+3