# Lesson 17

Interpreting Function Parts in Situations

- Let’s pick apart functions

### 17.1: Math Talk: Function Evaluation

Mentally find the value of \(x\) for the given function value using the function: \(f(x) = 3(x-2)\)

\(f(x) = 9\)

\(f(x) = 210\)

\(f(x) = 10\)

\(f(x) = 0\)

### 17.2: A Long Car Trip

On a long car trip, the distance on the odometer (in miles) is a function of time (in hours after the trip begins) given by the equation \(d(t) = 34t + 45,\!233\).

- What is the rate of change for the function? What does it mean in this situation?
- What is the value of \(d(0)\)? What does it mean in this situation?
- What is the value of \(d(\text{-}1)\)? What does it mean in this situation?
- When is \(d(t) = 45,\!800\)?
- Do each of the values make sense? Explain your reasoning.

### 17.3: A Warehouse and Highway

- A warehouse in a factory initially holds 2,385 items and receives all of the items made in production throughout a day. During a particular day, the factory produces 150 items per hour to put into the warehouse. Write a function, \(f\), to represent the number of items in the warehouse at time \(t\) after production begins for the day.
- What are the units for \(t\)?
- What is the domain of the function? Explain your reasoning.
- What is the range of the function? Explain your reasoning.
- What is the value of \(t\) when \(f(t) = 3,\!000\)? What does that mean in this situation?

- During a focused effort on building new infrastructure for 3 years, a company can build 0.8 miles of highway per day. The company has already built 12 miles of highway before the focused effort. Write a function, \(g\), to represent the length of highway built by the company as a function of \(t\) during the focused effort.
- What are the units for \(g(t)\)?
- What is the domain of the function? Explain your reasoning.
- What is the range of the function? Explain your reasoning.
- What is the value of \(t\) when \(g(t) = 400\)? What does that mean in this situation?