# Lesson 4

Interpreting Functions

- Let’s interpret some functions.

### 4.1: Math Talk: Finding Outputs

Mentally evaluate the output for the input of 3.

\(f(x) = 4\left( x - \frac{1}{2}\right)\)

\(g(x) = 2(6 - x)\)

\(h(x) = \frac{5}{3}x + \frac{1}{3}\)

\(j(x) = 0.2x - 1\)

### 4.2: It’s Getting Hotter

A machine in a laboratory is set to steadily increase the temperature inside. The temperature in degrees Celsius inside the machine after being turned on is a function of time, in seconds, given by the equation \(f(t) = 22 + 1.3t\).

- What does \(f(3)\) mean in this situation?
- Find the value of \(f(3)\) and interpret that value.
- What does the equation \(f(t) = 35\) mean in this situation?
- Solve the equation to find the value of \(t\) for the previous question.
- Write an equation involving \(f\) that represents each of these situations:
- The temperature in the machine 30 seconds after it is turned on.
- The time when the temperature inside the machine is 100 degrees Celsius.

### 4.3: You Charge How Much?

- Which line represents \(y = f(t)\)? Explain how you know.
- The lines intersect at the point \((4,900)\). What does this point mean in this situation?
- Which is greater, \(f(10)\) or \(g(10)\)? What does that mean in this situation?
- Your group has $1,500 to spend on supercomputer time. Which company should your group use?
- Explain or show your reasoning using the equations.
- Explain or show your reasoning using the graph.