Module 7: Rational Functions and Function Operations

 

Interpreting graphs when multiplying or dividing functions is similar to interpreting graphs when adding or subtracting functions. Try This 2 explores this idea further.

 

Try This 2

 

Open Lesson 5 Printable Template. Either make a sketch of the graph or print the graph to complete the following activity.

 

 

This is a graph of two linear functions. The function f at x passes through points (0, negative 1) and (4, 1), and the function g at x passes through points (0, 0) and (4, 1).


    1. Use the graph to sketch h(x) = (fg)(x). Explain the procedure you used.
    2. Predict where any vertical asymptotes for and will occur. How are these asymptotes related to the non-permissible values of p(x) and q(x)?
    3. Sketch p(x) and q(x).

    1. What type of functions are h(x), p(x), and q(x)? Explain.
    2. State the domain for h(x), p(x), and q(x).

course folder Save your responses in your course folder.

Asymptotes occur at non-permissible values where the denominator is equal to zero. For what x-values will the denominators be zero?
This can be done pointwise. Pick a point from each function with the same x-value and either multiply or divide the y-values.
Using multiple colours or multiple graphs will make your graphs easier to interpret.