October 24, 2013
Graph of a Rational Function
1. End behavior asymptote:
N < D then horizontal asymptote is y = 0
N=D
then horizontal asymptote is leading coefficient of numerator
y = leading coefficient of denominator
N>D
then no horizontal asymptote, but a quotient
asymptote: y = q(x)
2. Vertical asymptotes: occur at zeros of
denominator, provided they are not also zeros of
the numerator.
3. x-intercepts: zeros of numerator, provided they are not
also zeros of the denominator.
4. y-intercept: the value of f(0), if defined.
October 24, 2013
Find the following. Then draw a sketch.
f(x) = 3x - 6
x+2
1. y-intercept
2. x-intercept(s)
3. vertical asymptotes
4. horizontal asymptotes
5. slant asymptotes
6. several points
October 24, 2013
Find the following. Then draw a sketch.
1. y-intercept
2. x-intercept(s)
3. vertical asymptotes
4. horizontal asymptotes
5. slant asymptotes
6. several points
Graph f(x) =
x3
x2- 9
October 24, 2013
Find the following. Then draw a sketch.
1. y-intercept
Graph f(x) = 2x2 - 2
2. x-intercept(s)
3. vertical asymptotes
4. horizontal asymptotes
5. slant asymptotes
6. several points
x2 - 4
October 24, 2013
Find the following. Then draw a sketch.
Graph
1. y-intercept
2. x-intercept(s)
3. vertical asymptotes
4. horizontal asymptotes
5. slant asymptotes
6. several points
f(x) = x - 3
x2 - 9
October 24, 2013
Graph f(x) = x3 - 3x2 + 3x + 1
x-1