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Numerical Substitution: f(x)=x^2-2

f(x) = 5 ; 25-2 = 23

Variable Substitution: f(x) = (w+6)

x^2-1/2 = (w+6)^2 - 1/2

Compound Functions: f(g(x))

Solve the inner equation then use result in outer equation.

Functions with Unknown Constants: If f(x)=ax^2-x and f(4)=28, what is f(-2)?

1. Solve for the unknown, in this case "a"

2. Rewrite the function. replacing the constant with numerical value.

3. Solve function for the new input variable.

2. Rewrite the function. replacing the constant with numerical value.

3. Solve function for the new input variable.

Function Graphs: Graph the function, f(x)=-2x^2+1

Use x inputs to determine y coordinates, then map.

Common Function Type #1: Direct Proportionality - Set up ratios for the "before" case and the "after" case, and then set the ratios equal to each other.

i.e. y=kx > k=y/x

Common Function Type #2: Indirect Proportionality - Set up products for the "before" case and the "after" case, and then set the products equal to each other.

i.e. y=k/x , k=xy

Common Function Type #2: Linear Growth or decay - Defines a constant rate of growth after a specified beginning point.

i.e. y=mx+b