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