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?

    graph 1

    graph, Starts with a balance of $700, each y coordinate is the fraction 3 over 10 greater than the previous y coordinate.

    graph 2

    Y intercept = 300, each point’s y coordinate is 30 less than previous point 

    graph 3

    Y intercept = 500, each point’s y coordinate is one tenth of previous point 

    graph 4

    Y intercept = 500, each point’s y coordinate is 15 more than previous point 

  3. To check, use technology to graph your equations. Make sure to use the same graphing window. Check that the graph of your equation matches the graph you chose.

Summary