The Spy Who Graphed Me

in The Spy Who Graphed Me

Graphs as functions Input/Output tables Graphing different functions Algebra walk Review Table of Contents

Functions • 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 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 • 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 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 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 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 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 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 • 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 • 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).

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The Spy Who Graphed Me