Pizza The area A, in square inches, of a pizza is a function of its radius r, in inches. The cost C, in dollars, of the sauce for a pizza is a function of the weight w, in ounces, of sauce used. Graph these functions shown by the tables below. Is each function linear or nonlinear?
Radius (in.), r |
Area
|
---|---|
2 | 12.57 |
4 | 50.27 |
6 | 113.10 |
8 | 201.06 |
10 | 314.16 |
Weight (oz), w | Cost, C |
---|---|
2 | $.80 |
4 | $1.60 |
5 | $2.40 |
8 | $3.20 |
10 | $4.00 |
Know | Need | Plan |
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The relationships shown in the tables are functions. | To classify the functions as linear or nonlinear | Use the tables to make graphs. |
How can a graph tell you if a function is linear or nonlinear?
The graph of a linear function is a nonvertical line or part of a line, but the graph of a nonlinear function is not.
Graph A as a function of r.
The graph is a curve, not a line, so the function is nonlinear.
Graph C as a function of w.
The graph is a line, so the function is nonlinear. function is linear.
The table below shows the fraction A of the original area of a piece of paper that remains after the paper has been cut in half n times. Graph the function represented by the table. Is the function linear or nonlinear?
Number of Cuts, n | 1 | 2 | 3 | 4 |
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Fraction of Original Area Remaining, A |
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