# 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 $$d(t) = 34t + 45,\!233$$.

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

### 17.3: A Warehouse and Highway

1. 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.
1. What are the units for $$t$$?
2. What is the domain of the function? Explain your reasoning.
3. What is the range of the function? Explain your reasoning.
4. What is the value of $$t$$ when $$f(t) = 3,\!000$$? What does that mean in this situation?
2. 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.
1. What are the units for $$g(t)$$?
2. What is the domain of the function? Explain your reasoning.
3. What is the range of the function? Explain your reasoning.
4. What is the value of $$t$$ when $$g(t) = 400$$? What does that mean in this situation?