Discover
Try This 1
Consider the functions f(x) = x + 1 and g(x) = −x + 3.
- Predict what the graph of p(x) = (fg)(x) will look like. Explain how you made this prediction.
- Predict what the graph of will look like. Explain how you made this prediction.
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- Use Multiply and Divide Functions to graph p(x) and q(x) and to check your predictions. Save screen captures of your two graphs.
- Explain how the graph of p(x) is related to the graphs of f(x) and g(x).
- Explain how the graph of q(x) is related to the graphs of f(x) and g(x).
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- Use the equations of f(x) and g(x) to write an equation for p(x) and for q(x) in terms of x. Explain how you determined equations for p(x) and q(x).
- Are there any restrictions on x for p(x) or q(x)? Explain.
- Do the graphs of the equations you determined match the graphs from Multiply and Divide Functions? Should they?
- Can the domain of p(x) or q(x) be determined from f(x)and g(x)? If so, explain how.
Save your responses in your course folder.
Share 1
With a partner or group, discuss the following questions based on the information in Try This 1.
- How are multiplying and dividing functions similar? How are they different?
- Compare multiplying and dividing functions to adding and subtracting functions. Describe both similarities and differences.
If required, save a record of your discussion in your course folder.