Functions&graphing 3.2

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Functions and Graphing Section 3.2

What is a Function? A

function is an equation in x and y such that for each value of x, the equation will provide you with a unique value of y Example: y=2x is a function because for each value of x, the equation gives a unique value of y. For example, if you plug it 2 for x, the equation gives you exactly one y value, y=4

What is a Function? However,

an equation such as y2=x is not a function. For example, if you plug it x=1, you get two values of y: ◦ Y=1 ◦ Y= -1

Functions We

can also think of this function as an input-output machine. If we give it an x value, it will chug out exactly one y value.

Graphing a Function In

order to graph a function, we can use a table to organize the information and then plot the points on a coordinate system and graph. Ex:x (Input) y (Output) y = 2x - 1 x  y –2

2(–2) – 1 = –5

–5

–1

2(–1) – 1 = –3

–3

0

2(0) – 1 = –1

–1

1

2(1) – 1 = 1

1

2

2(2) – 1 = 3

3

3

2(3) – 1 = 5

5

Graphing x

(Input) –2 –1 0 1 2 3

x y

2(– 2) – 1 = –5 2(– 1) – 1 = –3 2(0) – 1 = – 1 2(1) – 1 =  1 2(2) – 1 =  3 2(3) – 1 =  5

y

(Output) –5 –3 –1 1 3 5

X

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