# 8.10: Trip Functions

**At Grade**Created by: CK-12

**Trip Functions – Complete Tables and Write Function Rules**

**Teacher Notes**

Students use facts to complete rate tables and write rules in words to describe the relationship between the input and the output. All functions are of the form of \begin{align*}y = a \cdot x + b\end{align*}, that is, the sum of an initial value (number of miles showing on odometers/pedometers before the start of a trip) and the product of number of hours traveled and average speed in miles per hour.

**Solutions:**

**Trip Functions 1**

Rule: Number of miles is the sum of 23,500 and the product of number of hours and 40 mph.

**Trip Functions 2**

Rule: Number of miles is the sum of 72,160 and the product of number of hours and 30 mph.

**Trip Functions – Complete Tables and Write Function Rules**

**Read the facts. Follow the steps.**

**Facts:** Before the start of the cross-country trip, the odometer in Mrs. Wilson’s car showed 4,100 miles. On the trip, she averaged 50 miles per hour.

**First:** Complete the table to show changes in Ms. Wilson’s odometer for the first 6 hours.

**Second:** Write a rule that describes how the number of hours traveled is related to what the car odometer shows.

Rule: _______________________________________________________

\begin{align*}& \mathbf{Describe:} && \text{Before the start of the trip, Ms. Wilson's car odameter showed} \ 4,100\\ &&& \text{miles. On the trip, she drove an average of} \ 50 \ \text{miles each hour. The table}\\ &&& \text{shows} \ 4,100 \ \text{miles at} \ 0 \ \text{hours.}\\ \\ & \mathbf{My \ Job:} && \text{Use the facts to complete the table. Write a rule that shows how the}\\ &&& \text{number of miles on the odometer is related to the number of hours of}\\ &&& \text{travel on the trip.}\\ \\ & \mathbf{Plan:} && \text{Start with the table. Add} \ 50 \ \text{to} \ 4,100 \ \text{for each new hour. Then write the}\\ &&& \text{rule.}\end{align*}

\begin{align*}& \mathbf{Solve:} && \text{Rule: Number of miles is the sum of} \ 4,100 \ \text{and the product of number of}\\ &&& \text{hours and} \ 50 \ \text{mph.}\\ \\ & \mathbf{Check:} && \text{Use the rule and to verify the facts.}\\ &&& 4,100 + 1 \times 50=4,150\\ &&& 4,100 + 2 \times 50=4,200\\ &&& 4,100 + 3 \times 50=4,250\\ &&& 4,100 + 4 \times 50=4,300\\ &&& 4,100 + 5 \times 50=4,350\\ &&& 4,100 + 6 \times 50=4,400\end{align*}

**Trip Functions 1**

**Facts:** Before he left on his trip, Mr. Patterson’s truck odometer showed 23,500 miles. He averaged 40 miles per hour on his drive from Sacramento to San Diego.

**First:** Complete the table to show changes in Mr. Patterson’s truck odometer for the first 6 hours.

**Second:** Write a rule that describes how the number of hours traveled is related to what the truck odometer shows.

Rule: _______________________________________________________

**Trip Functions 2**

**Facts:** The Karene City School Bus averaged 30 miles per hour on its trip to the state basketball competition. At the start of the trip, the bus’s odometer showed 72,160 miles.

**First:** Complete the table to show changes in the bus’s odometer for the first 6 hours.

**Second:** Write a rule that describes how the number of hours traveled is related to what the bus odometer shows.

Rule: _______________________________________________________

*Extra for Experts:***Trip Functions – Complete Tables and Write Function Rules**

**Trip Functions Extra 1**

**Facts:** Charlie’s pedometer is on his belt. It registers the number of miles walked. Before the hike, the pedometer showed 27 miles. Charlie hiked for several days and averaged 3 miles per hour.

**First:** Complete the table to show changes in Charlie’s pedometer for the first 6 hours.

**Second:** Write a rule that describes how the number of hours traveled is related to what the pedometer shows.

Rule: _______________________________________________________

**Trip Functions Extra 2**

**Facts:** Before Brent left on his bike hike, his bike’s odometer showed 62 miles. Brent averaged 8 miles per hour.

**First:** Complete the table to show changes in Brent’s bike odometer for the first 6 hours.

**Second:** Write a rule that describes how the number of hours traveled is related to what the bike odometer shows.

Rule: _______________________________________________________

**Solutions:**

**Trip Functions Extra 1**

Rule: Number of miles is the sum of 27 and the product of number of hours and 3 mph.

**Trip Functions Extra 2**

Rule: Number of miles is the sum of 62 and the product of number of hours and 8 mph.

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