# Create and Graph Rational Functions

Videos and lessons to help High School students learn how to create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

### Suggested Learning Targets

• Create equations in two or more variables to represent relationships between quantities.
• Graph equations in two variables on a coordinate plane and label the axes and scales.

Common Core: HSA-CED.A.2

Related Topics:
Algebra Word Problems

Common Core (Algebra)

Common Core for Mathematics

Creating and graphing equations in two or more variables (Common Core A-CED.2)
In this lesson you will learn how to create and graph relationships by using rational functions.

Model rational functions by drawing graphs - A-CED.2
Inverse variation; xy = k

Create equations in two or more variables to represent relationships between quantities (A-CED.2)
In this lesson you will learn how to create an equation for a simple rational function by using a graph and a table of values.

Rational Function Applications
1. Stephanie can jog 5 miles downhill in the same time it takes her to jog 3 miles uphill. She jogs downhill 4 mph faster than she jogs uphill. Fins her jogging rate each way.
2. Adrian can weed the garden twice as fast as his son, Phlilip. Together, they can weed the garden in 3 hours. How long would it take each of them working alone?

Word Problems with Rational Equations
How to solve word problems involving rational equations, such as work problems.
1. Sandra can paint a kitchen in 6 hours and Roger can paint the same kitchen in 7 hours. How long will it take for both working together to paint the kitchen?
2. Together, Naomi and Kenyu can write a particular type of computer program in 17 hours. Alone, Naomi can do the job 3 hours faster than Kenyu. Find the time that each person takes to write a computer program.

Rational Equations Word Problems
Solving 'work' problems with rational equations.

Rational Equations Word Problems
Solving 'distance' problems with rational equations.

Modeling with Rational Functions
1. A speedboat can travel 32 mph in still water. It travels 150 miles upstream against the current and then returns to the starting location. The total time of the trip is 10 hours. What is the speed of the current?
2. Bill can finish a report in two hours. Maria can finish the report in four hours. How long will it take them to finish the report if they work together?

Rational Functions
An introduction to rational functions, the reciprocal function, and vertical and horizontal asymptotes.

Graphing Rational Functions
A couple of examples on graphing rational functions.

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