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

(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 it started burning.

Equation to find ordered pairs; if x= hours and y= inches then F(x)= 9-x(0.5) so
(1)(1,8.5)
(2)(2,8.0)
(3)(3,7.5)
(4)(4,7.0)
(5)(5,6.5)
(6)(6,6.0)

(B) Is this relation a function? Answer: Yes this is a linear function because the equation is linear, when plotted the line is straight with a negative slope.

(C) If F(x)= 9-x(0.5) Then

(1)(1,8.65)
(2)(2,8.20)
(3)(3,7.75)
(4)(4,7.30)
(5)(5,6.85)
(6)(6,6.40)