Algebra II/Trig Honors
Unit 5 Day 2: Graph Simple Rational Functions
Objective: To graph rational functions with and without translations
Definition:

Rational Function - _______________________________________________________
a
o The inverse variation function f  x   is a rational function.
x
Parent Function for Simple Rational Functions:
1
The graph of the parent function f  x   is a _________________________, which consists of
x
two symmetrical parts called _____________________.
*Any function of the form g x  
function f  x  
a
x

Domain: ____________________

Range: _____________________

Vertical Asymptote: ___________

Horizontal Asymptote: _________
a  0 has the same asymptotes, domain, and range as the
1
.
x
Example 1: Graph a rational function of the form y 
Graph the function y 
a
x
6
1
. Compare the graph with the graph of y  .
x
x
Step 1: Draw the asymptotes x  0 and y  0 .
Step 2: Plot points on either side of the
vertical asymptote.
Step 3: Draw the branches of the hyperbola
passing through the points and
approaching the asymptotes.
Example 2: Graph a rational function of the form y 
Graph the function y 
a
k
xh
4
 1 . State the domain and range.
x2
Step 1: Draw the asymptotes x  2 and y  1 .
Step 2: Plot points on either side of the
vertical asymptote.
Step 3: Draw the branches of the hyperbola
passing through the points and
approaching the asymptotes.
Domain: _________________
Range: ___________________
Practice: Graph the function. State the domain and range.
a.
y
b. f  x  
8
5
x
Domain: _______
Range: ________
1
2
x3
Domain: _______
Range: ________
Other Rational Functions: All rational functions of the form y 
ax  b
also have graphs that
cx  d
are hyperbolas.

The vertical asymptote of the graph is the line _____________ because the function is
undefined when the denominator __________ is zero.

The horizontal asymptote is the line ___________.
Example 3: Graph a rational function of the form y 
Graph y 
2x  1
. State the domain and range.
x3
ax  b
cx  d
Domain: ___________
Range: ____________
Example 4: Solve a multi-step problem
A 3-D printer builds up layers of material to make three-dimensional models. Each deposited
layer bonds to the layer below it. A company decides to make small display models of engine
components using a 3-D printer. The printer costs $24,000. The material for each model costs
$300.
 Write an equation that gives the average cost per model as a function of the number of
models printed.
 Graph the function. Use the graph to estimate how many models must be printed for the
average cost per model to fall to $700.
 What happened to the average cost as more models are printed?
HW: Page 313 #3-21 (M3), 27-33 (odd), 38