# 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 $$f(t) = 22 + 1.3t$$.

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

### 4.3: You Charge How Much?

Two companies charge to rent time using their supercomputers. Their fees are given by the equations $$f(t) = 500 + 100t$$ and $$g(t) = 300 + 150t$$. The lines $$y = f(t)$$ and $$y = g(t)$$ are graphed.

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