function tables and graphs. function a function is when each input (x-value) corresponds to exactly...
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Function Tables and Graphs
Function
• A function is when each input (x-value) corresponds to exactly one output (y- value)
• In other words, when you substitute (x) into an equation there is only one possible answer (y)
Let me show you what I mean• Let’s use the function y = 2x + 5
y = 2(0) + 5 if x = 0 y = 5
x y
0 5
2
5
10
20
Fill in the function table for the function y = 4x – 3
x y
0
2
5
10
20
Fill in the function table for the function y = 4x – 3
x y
0 -3
2 5
5 17
10 37
20 77
Fill in the function table for the function y = -3x + 5
x y
0
2
5
-2
-5
Fill in the function table for the function y = -3x + 5
x y
0 5
2 -1
5 -10
-2 11
-5 20
This should be an Olympic sport!
Fill in the function table for the function y = x - 4
x y
0
2
5
-2
-5
Fill in the function table for the function y = x - 4
x y
0 -4
2 -3
5 -1
-2 -5
-5 -6
Graphing a Function from a Function Table
• When given a function you can graph it by creating a function table and plotting the points you generate.
• You can pick any points for x and substitute them into the function for the output y
• You should plot at least 5 points to get a good idea of what your graph looks like: 0, two positive numbers, and two negative numbers.
Let’s Use the Functions We Worked With Earlier
y = 2x + 5
x y
0
2
5
-2
-5
Let’s Use the Functions We Worked With Earlier
y = 2x + 5
x y
0 5
2 9
5 15
-2 1
-5 -5
y = 4x – 3
x y
0
2
5
-2
-5
y = 4x – 3
x y
0 -3
2 5
5 17
-2 -11
-5 -23
Two of our points go way off our graph.It helps to show how steep the slope is.
y = -3x + 5
x y
0
2
5
-2
-5
y = x - 4
x y
0
2
5
-2
-5
Closure
• With a partner, graph the function y = -3x + 3
y = -3x + 3
x y