Functions: Apply

Question

Targeted Activity
Level 1
Record the hourly temperature for a period of six hours of any day of your choosing, and fill out the following table.

For example, you can choose to record the hourly temperature from 6am to 12pm, 9am to 3pm, or 1pm to 7pm.

Time (hours after your initial recording) Temperature (Degrees Fahrenheit)
0

1

2

3

4

5

6

This table represents the function of temperature over time.

What is the initial value of this function? Interpret its meaning.
Choose two pairs of (x,y)
values, and find two values of the rate of change based on these two pairs of (x,y)
values.
Graph the function and determine if the function is a linear function. Is your conclusion consistent with the rate of change you found in question 2?




Reveal Answer
Level 2
For her vacation, Blake wants to rent a bicycle to explore the city. The rental service charges a one-time fee and an additional daily rate for each rental bike. They offer two packages: $32 for a three-day rental, or $41 for a five-day rental.

Find the one-time fee and the daily rate for this rental service.
Write the linear function representing the relationship between the amount of money spent on bicycle rental and the number of days she rents the bike.




Reveal Answer
Level 3
Review the contents of the lessons in the unit. Then go back to the Check-In and Practice exercises and try them again.

View Learning Coach Guide

Answer 1

Level 1

Initial value of the function: The initial value of the function is the temperature you recorded at Time 0. It represents the starting point of the temperature over time.

Two pairs of (x,y) values:

1. (0, 70) - This means the temperature at the start of recording was 70 degrees Fahrenheit.
2. (3, 75) - This means the temperature after 3 hours was 75 degrees Fahrenheit.

Rate of change:

Using the pairs of (x,y) values:
(3 hours) - (0 hours) = 3 hours
(75 degrees) - (70 degrees) = 5 degrees

Rate of change = Change in temperature / Change in time
Rate of change = 5 degrees / 3 hours ≈ 1.67 degrees per hour

Graphing the function:
If the temperature over time is a straight line, then it is a linear function. The graph will determine if the function is linear or not. If the rate of change is constant, then the function is linear.