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PRACTICE Elizabeth throws a ball in the air and records the ball’s height over time. Her data are shown in...

9. PRACTICE Elizabeth throws a ball in the air and records the ball’s height over time. Her data are shown in the table.
Time (sec) | Height (ft)
0.0 | 0
0.5 | 12
1.0 | 20
1.5 | 24
2.0 | 24
2.5 | 20
3.0 | 12
3.5 | 0
a. Is the relationship between time and the height of the ball a function? Why or why not?
b. Is the relationship between time and the height of the ball a linear function? Why or why not?

Answer

9a. Yes. Each time corresponds to exactly one height, so the relationship is a function.

9b. No. For equal time intervals of 0.5 second, the changes in height are 12, 8, 4, 0, −4, −8, and −12 feet. These changes are not constant, so the function is not linear.

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