Question

64 POINTS

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

Part A: {(0,9),(1,8.5),(2,8),(3,7.5),(4,7),(5,6.5)}

Part B: This relation is a function, because each x input has it's own y output.

Part C: Yes, the relation would still be a function as the y-coordinate is not repeating itself for different x-coordinates. Decreasing the number of this rate of change does not affect whether the relation is a function or not.

Good luck on your test! I hope I helped :)

Answer 2

L(t)=9-0.5t
t=time in hours,
L(t)=length of candle at time t

(A) substitute t=1,2,3,4,5,6 respectively to get
(1,8.5)
(2,8)
(3,7.5)
(4,7)
(5,6.5)
(6,6)

(B) it is a function because none of the x-values duplicate, (nor the y-values).

(C) If the rate changes to 0.45 "/hr, the relation is still linear.
All linear function with finite slope are functions.