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.
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.