# Lesson 12

Connections between Graphs and Equations

• Let’s examine some situations, equations, and graphs.

### 12.1: Math Talk: Evaluating a Function

Here is a function: $$g(x)=100-5x$$

Evaluate mentally:

$$g(0)$$

$$g(1)$$

$$g(4)$$

$$g(20)$$

### 12.2: Bank Accounts

Each function represents the amount in a bank account after $$t$$ weeks.

$$A(t) = 500$$

$$B(t) = 500 + 40t$$

$$C(t) = 500 - 40t$$

$$D(t) = 500 \boldcdot (1.5)^t$$

$$E(t) = 500 \boldcdot (0.75)^t$$

1. Make a table for each bank account showing the money in the account at 0, 1, 2, and 3 weeks.
2. Describe in words how the money in the account is changing week by week.
3. Use technology to create a graph of each function. How can you see your description in each graph?

### 12.3: Build a New Function

Consider the same five functions:

$$A(t) = 500$$

$$B(t) = 500 + 40t$$

$$C(t) = 500 - 40t$$

$$D(t) = 500 \boldcdot (1.5)^t$$

$$E(t) = 500 \boldcdot (0.75)^t$$

1. Starting with one of the functions, change it so that it represents an account that . . .
1. Starts with a balance of $300, and loses$40 each week.
2. Starts with a balance of $500, and gains$15 each week.
3. Starts with a balance of $500, and loses $$\frac{1}{10}$$ of its value each week. 4. Starts with a balance of$700, and gains $$\frac{3}{10}$$ of its value each week.
2. Here are four graphs. Which graph matches each of your new equations?