Question

A candle burns down at the rate of 0.5 inches per hour. The original height of the candle was 9 inches.

Part A: Write a list of 6 ordered pairs to show the height of the candle in inches (y) as a function of time in hours (x) from the first hour after it started burning. For example, the point (0, 9) would represent a height of 9 inches after 0 hours. Explain how you obtained the ordered pairs. (5 points)

Part B: Is this relation a function? Justify your answer using the list of ordered pairs you created in Part A. (2 points)

Part C: If the rate at which the candle burned was 0.45 inches per hour instead of 0.5 inches per hour, would the relation be a function? Explain your answer using input and output values. (3 points)

Answer 1

You can get those ordered pairs subtracting 9-0.5, then that result minus 0.5 because from the rate the candle reduces its height 0.5inches per each hour.Part B: Is this relation a function? Yes, because each value of x has a single result or output in “y” (image)Part C: Yes, only difference is the time, the candle reduces its height 0.45 inches per each hour, examples of ordered pairs: (0,9) (1,8.55) (2,8.1)

Answer 2

A) Function would be: (0, 9) (1, 8.5) (2, 8) (3, 7.5) (4, 7) (5, 6.5) (6, 6)

Increase x-coordinate by 1 at each instance (time is increasing in hours) and decrease y-coordinate by 0.5 (height is decreasing)

B) Ordered Pairs: (0, 9) (1, 8.5) (2, 8) (3, 7.5) (4, 7) (5, 6.5) (6, 6)

As y-coordinate is not repeating for different x-values, "It is a Function"

C) Ordered Pairs: (0, 9) (1, 8.55) (2, 8.10), (3, 7.65), (4, 7.20), (5, 6.75)

Again, "It is a Function" as y-coordinate is not repeating for different y-'s. We've just decreased the y's, it doesn't affect x-coordinate, so the nature of our function won't change

Hope this helps!