4-3 Patterns and Nonlinear Functions

Quick Review

A nonlinear function is a function whose graph is not a line or part of a line.

Example

The area A of a square field is a function of the side length s of the field. Is the function linear or nonlinear?

Exercises

Graph the function shown by each table. Tell whether the function is linear or nonlinear.

10. x	y
    1	0
    2	1
    3	8
    4	20

11. x	y
    1	0
    2	4.5
    3	9
    4	13.5

12. x	y
    1	2
    2	6
    3	12
    4	72

13. x	y
    1	− 2 negative 2
    2	− 9 negative 9
    3	− 16 negative 16
    4	− 23 negative 23

4-4 Graphing a Function Rule

Quick Review

A continuous graph is a graph that is unbroken. A discrete graph is composed of distinct, isolated points. In a real-world graph, show only points that make sense.

Example

The total height h of a stack of cans is a function of the number n of layers of 4.5-in. cans used. This situation is represented by h = 4.5 n . h equals 4.5 n .  Graph the function.

Exercises

Graph the function rule. Explain why the graph is continuous or discrete.

14. Walnuts Your cost c to buy w pounds of walnuts at $6/lb is represented by c = 6 w . c equals 6 w .
15. Moving A truck originally held 24 chairs. You remove 2 chairs at a time. The number of chairs n remaining after you make t trips is represented by n = 24 − 2 t . n equals 24 minus 2 t .
16. Flood A burst pipe fills a basement with 37 in. of water. A pump empties the water at a rate of 1.5 in./h. The water level l, in inches, after t hours is represented by l = 37 − 1.5 t . l equals 37 minus 1.5 t .
17. Graph y = − | x | + 2 . y equals negative vertical line x vertical line plus 2 .

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