It is possible to predict what the graph of a function that was produced by adding or subtracting two other functions will look like. Try This 3 explores this idea.

Try This 3

Consider the following two functions:

1. Predict what graphs of the functions h(x) = (f + g)(x) and p(x) = (f − g)(x) will look like.
2. Use the graphs of f(x) and g(x) to complete a table like the following.
   
   

   x	f(x)	g(x)	h(x) = (f + g)(x)	p(x) = (f − g)(x)	q(x) = (g − f)(x)
   −2	−2	undefined
   −1	−1	undefined
   0	0	undefined
   1	1	−4
   2	2	0
   3	2.5	4
   4	3	3
   5	3.5	2
   6	4	1
   7	4	2.7
   8	4	3
   9	4	2.7
   10	undefined	1

3. Either print the Printable Template or make a sketch of the information. Then use this data to sketch h(x), p(x), and g(x).
   
4.  
   1. Describe a strategy you could use to graph h(x) given the graphs of f(x) and g(x).
   2. Describe a strategy you could use to graph p(x) given the graphs of f(x) and g(x).
5.  
   1. Describe how the domain and range of f(x) and g(x) are related to the domain and range of h(x), p(x), and q(x).
   2. Describe the relationship between the graph of p(x) and the graph of q(x).

Save your responses in your course folder.

Share 3

With a partner or group, discuss the following question based on your graphs created in Try This 3:

Describe a rule to determine the domain of r(x) using s(x) and t(x) if r(x) = s(x) + t(x).

If required, save a record of your discussion in your course folder.