Rational Functions and Inequalities

Question 1

dx² + ex + f

Answer 1

y intercept c/f
top fraction roots are roots
bottom fraction roots are x = assymptotes
a/d is horizontal assymptotes

Question 2

How do you find the oblique assymptote?

Answer 2

Do ax²/dx to find what line is parallel to
Divide bottom fraction by top to get quotient and remainder
As x → ∞, remainder → 0 so y = quotient

Question 3

How do you plot the graph of 1 / f(x)?
when f(x)= ±1
when f(x)=0
when f(x) → ∞
horizontal assymptote at y=b
y intercept at c

Answer 3

when f(x)= ±1                       1/f(x)= ±1
when f(x)=0                         1/f(x) vertical assymptote
when f(x) → ∞                      1/f(x) → 0
horizontal assymptote       1/f(x) horizontal a. at y=1/b
y intercept                          1/f(x) y interceot at 1/c

Question 4

|f(x)/g(x)|

Answer 4

|g(x)|

Question 5

a|f(x)|

Answer 5

|af(x)|

Question 6

How do turning points differ from y=f(x) to 1/f(x)?

Answer 6

min → max
(-a,c) → (-a, 1/c)
max → min
(d,e) → (d, 1/e)