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Presentation Transcript

Input/Output tables

Graphing different functions

Algebra walk

Review

Table of Contents

- Equations that are written in the form y= 3x + 4 where x is a variable are called functions. We can think of them almost as little machines. We put in something for x and we get a value for y.
- We use the terms input and output to describe the x and the y values. The function is a rule that acts on the numbers.

- Let’s look at an example of how it works: our rule (function) is y = 2x + 1
- X Y

Y= 2x + 1

11

5

Input

Output

2(5) + 1

Making an Input Output Table (function) is y = 2x + 1

Y = 2x + 1

- Using our same function y= 2x + 1 we can make an input output table. For each value of x (input) that appears calculate the resulting y (output).

x

y

5

2

9

4

13

6

-3

-5

y (function) is y = 2x + 1

- Let’s see what this rule looks like on a more traditional looking graph.

Y = 2x + 1

X

Y

x

0

1

1

3

2

5

3

7

Making an Input Output Table (function) is y = 2x + 1

Y = - 2x

- Let’s try graphing with a different function y = -2x.
- The first thing we need of course is our rule, which we have written above.
- Can you predict how this line will look when we graph it.

Making an Input Output Table (function) is y = 2x + 1

Y = -2x

- Using our same function y= -2x we can make an input output table. For each value of x (input) that appears calculate the resulting y (output).

x

y

-4

2

-8

4

-12

6

-3

6

Y = -2x (function) is y = 2x + 1

y

- Let’s see what we get when we graph this function on a more traditional looking graph.

X

Y

0

0

x

1

-2

2

-4

3

-6

-3

6

Making an Input Output Table (function) is y = 2x + 1

2

Y = X

- Using a different function y= X
- we can make an input output table. For each value of x (input) that appears calculate the resulting y (output).

x

y

2

4

2

3

9

0

0

-3

9

Word-up (function) is y = 2x + 1

y

2

Y = X

- Let’s see what this rule looks like on a more traditional looking graph.

X

Y

0

0

x

2

4

3

9

-2

4

-3

9

Let's Review (function) is y = 2x + 1

- Write down your equation in a:
- y= _ X + number format. This is sometimes called a y=mx+b equation (or linear) where m and b are numbers and x is a variable.
- In our equation y= 2x + 1, the 2 is the m and the 1 is the b.

Let’s Review (function) is y = 2x + 1

- Make an input output table using your equation (or function). Try different numbers for x and write down the corresponding numbers you get for y.
- Plot the points using their x and y numbers.
- Connect the points using a straight line.
- Make sure you try a 0 for x as that will help you find the Y intercept (where the line of the graph crosses the y axis).

The End (function) is y = 2x + 1

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