GRAPHING RATIONAL FUNCTIONSADV122
We have graphed several functions, now we are adding one more to the list!
Graphing Rational Functions
GRAPHING RATIONAL FUNCTIONSADV122
f(x) = + ka
x – h
(-a indicates a reflection in the x-axis)
vertical translation(-k = down, +k = up)
horizontal translation(+h = left, -h = right)
Pay attention to the transformation clues!
Watch the negative sign!! If h = -2 it will appear as x + 2.
GRAPHING RATIONAL FUNCTIONSADV122
Asymptotes
Places on the graph the function will approach, but will never touch.
GRAPHING RATIONAL FUNCTIONSADV122
f(x) =
1x
Vertical Asymptote: x = 0Horizontal Asymptote: y = 0
Graph:
A HYPERBOLA!!
No horizontal shift.No vertical shift.
GRAPHING RATIONAL FUNCTIONSADV122
Graph: f(x) = 1
x + 4
Vertical Asymptote: x = -4
x + 4 indicates a shift 4 units left
Horizontal Asymptote: y = 0
No vertical shift
GRAPHING RATIONAL FUNCTIONSADV122
Graph: f(x) = – 31x + 4
x + 4 indicates a shift 4 units left
–3 indicates a shift 3 units down which becomes the new horizontal asymptote y = -3.
Vertical Asymptote: x = -4
Horizontal Asymptote: y = 0
GRAPHING RATIONAL FUNCTIONSADV122
Graph: f(x) = + 6x
x – 1
x – 1 indicates a shift 1 unit right
+6 indicates a shift 6 units up moving the horizontal asymptote to y = 6
Vertical Asymptote: x = 1
Horizontal Asymptote: y = 1
GRAPHING RATIONAL FUNCTIONSADV122
Vertical Asymptotes (easy one) Set the denominator equal to zero
and solve for x. Example:
x-3=0 x=3
So: 3 is a vertical asymptote.
GRAPHING RATIONAL FUNCTIONSADV122
Horizontal Asymptotes (H.A) In order to have a horizontal
asymptote, the degree of the denominator must be the same, or greater than the degree in the numerator.
Examples: No H.A because Has a H.A because 3=3. Has a H.A because
GRAPHING RATIONAL FUNCTIONSADV122
If the degree of the denominator is GREATER
than the numerator.
The Asymptote is y=0 ( the x-axis)
GRAPHING RATIONAL FUNCTIONSADV122
If the degree of the denominator and
numerator are the same: Divide the leading coefficient of the numerator by the leading coefficient of the denominator in order to find the horizontal asymptote.
Example: Asymptote is 6/3 =2.
GRAPHING RATIONAL FUNCTIONSADV122
If there is a Vertical Shift The asymptote will be the same
number as the vertical shift. (think about why this is based on the
examples we did with graphs)
Example:
Vertical shift is 7, so H.A is at 7.
GRAPHING RATIONAL FUNCTIONSADV122
Homework
http://www.kutasoftware.com/FreeWorksheets/Alg2Worksheets/Graphing%20Simple%20Rational%20Functions.pdf