Linear functions have to come in the form y=mx+b, or in the forms mx+y=b, in that case, solve the expression to isolate y. Linear functions form a linear line in the graph. If the slope is pointing towards the right hand corner at its top, m is positive, if the slope if pointing at the top right corner at its top, then m is negative. y=x or y=b is when m is 1 or 0 and b=0. y=b forms a line with no angle. M is the slope of a function, b is the y intercept. Below is the explanation of different functions. Scroll down.

If you only have a graph and you don't know the function, we can find the function through slope formulas. m= Δy/ Δx. You plot 2 points on the line, their coordinates will be (x1,y1) (x2,y2).  Δy=y2-y1 and  Δx=x2-x1, and there, that's how to find slope. b is the y intercept, (0,b), and you take the y value and plug it in your equation. The one above is y=2x+2 and it is positive. You can try in the same way. As we progress into harder math, y usually becomes f(x), stands for function of x. FOr the previous example 2x+2, f(1)=4.

To identify a linear function in a info graph, see the difference between each of the x value and that gets divided by the corresponding y differential. If this is confusing, look down.

Domain is x and range is y for a linear function. (note for readers)

Inverse functions are functions that undo a function. f^-1(f(x))=x

To inverse a function, inverse all the operations. example: y=2x-2, 2x= 2*x, now it becomes x/2. -2 is subtraction, we turn it to addition, and now its +2, so the inverse of y=2x-2 is y=(x+2)/2.

y=3x+9 is y=(x-9)/3.

Piecewise linear functions:

A piece wise linear function is a linear function but x belongs or is between a interval. Resulting in non infinite lines or functions.

∈ is the belong to symbol, it shows what things are belonged to. 3 ∈[1,9]  you ∈[parents].

In a piecewise function, we use x<, x>, x ≤, x ≥, x ≠, x=, x∈ signs. below is an example:

Vertical line test:

The vertical line test is used to determine if a graph is a function of not, draw a vertical line through the center of the function, if it intercepts more than once with the so called function, then that is not a function. It's only supposed to intercept it once. look below:

Notes for readers:

A linear function y=mx+b is horizontal when m=0. (constant function)

The domain and range of a linear function is all real numbers (R)(coz its infinite) whereas the range of a constant function is b.

A constant function has no inverse.

2 functions are parallel if there slopes are equal.

2 functions are perpendicular if the product of there slopes is -1.

A vertical line is not a function(doesn't pass vertical line test)