**Composition operation:** means putting one function into another

Syntax:

f(x) = f[g(x)]

g(x) = g[f(x)]

The bigger letter is the function that is the external one

[ ], just means nothing and is just normal parentheses (), not something special

OR F(x) = f[z = g(x)], where z is just the variable for the bigger function (not important at all)

**Identification of a graph that gets changed**, like reflected over the x-axis is to simply take the f(x)/y value and plug it into the new function and see which function gives you the right answer back

**Variation:****Direct variation:**

**Inverse variation:**

**The Vertical-Line Test:**

If you add a vertical line to a function anywhere, and it hits the function more than once, then it is NOT a function

**Absolute value equations:**

The way to solve an absolute value is to have two versions of the function

Ex.

|x-3|= 8

x-3 = 8 AND -(x-3) = 8

x = 11 and x = -5

ALSO

You can’t get a negative value of an absolute value equation

Ex.

|x-1| = -1, has no solution

**The theory behind zeros:**

**c** is just used as a representation of the x-value that creates the zero

**Piecewise functions:**

Smaller functions into one function, with their own sub-domains

**Greatest Integer Function:**

That weird door step function

Doesn’t have any decimal values only integers

**How to decompose a composition of functions:**

Just look at the function and find a possible g(x) and f(x)

**Jointly variation Example:**

And then you can find y, when you know x, z and now k too

**Invertible Functions:**

A function that only has unique x and y values

Ex.

Quadratic functions are not invertible, but linear ones are

## No Responses