McGraw Hill Lesson 9-4 graphing rational functions

if f(x) = a(x)/b(x), a(x) and b(x) are polynomial functions with no common factors other than 1, and b(x) DOES NOT EQUAL ZERO

f(x) has a vertical asymptote whenever

b(x) = 0

if f(x) = a(x)/b(x), a(x) and b(x) are polynomial functions with no common factors other than 1, and b(x) DOES NOT EQUAL ZERO

f(x) has at most ____ horizontal asymptote

if the degree of a(x) is greater than the degree of b(x), there is

one

no horizontal asymptote

if f(x) = a(x)/b(x), a(x) and b(x) are polynomial functions with no common factors other than 1, and b(x) DOES NOT EQUAL ZERO

f(x) has at most ____ horizontal asymptote

ig the degree of a(x) is less than the degree of b(x), the horizontal asymptote is the line

one

y=0

if f(x) = a(x)/b(x), a(x) and b(x) are polynomial functions with no common factors other than 1, and b(x) DOES NOT EQUAL ZERO

f(x) has at most ____ horizontal asymptote

if the degree of a(x) equals the degree of b(x), the horizontal asymptote is the line

one

y= leading coefficient of a(x) / leading coefficient of b(x)

graph:

f(x) = x^4/6x+12

graph:

f(x) = x^4-16/x²-1

graph:

f(x) = x³/8x-4

graph:

f(x)= x³ + 64 / 16x - 24

what do you do to find the vertical asymotope?

set the denominator to 0

find the vertical asymptote of y= 1 / x - 3

3

how to find the horizontal asymptotes?

1 - what half of the fraction is to the highest power?

2

…denominator higher, y=0

…numerator higher, do the fraction

what is the vertical asymptote of 6x - 18 / 2x + 4

-2

find the horizontal asymptote of y = 6x - 18 / 2x + 4, and why?

3, because 6x/2x is 3

domain cannot be….

vertical asymotope

range cannot be…

horizontal asymotope

if the vertical asymptote is at 3, how would you write the domain?

(-INFINITY, 3) u (3, INFINITY)

what is the vertical asymptote of y = 1 / x+2 + 7

-2

what is the horizontal asymptote of y = 1 / x+2 + 7, and why?

7, because it shifted up seven units

find the x and y intercepts of 6x - 18 / 2x + 4

x-int = (3, 0)

y-int = (0, -4.5)

how to find x-int of an equation?

set numerator to equal 0

how to find y-int of equation?

set x to 0

find domain and range of y = 6x - 18 / 2x + 4

D(-INFINITY, -2) U (-2, INFINITY)

R(-INFINITY, 3) U (3, INFINITY)