Advanced Math / Nonlinear Functions
Nonlinear Functions
Parameter questions for nonlinear functions may use vertex form, domain restrictions, exponential factors, or input-output conditions.
Least you need to know
- For $f(x)=a(x-h)^2+k$, the vertex is $(h,k)$.
- For $f(x)=ab^x$, $a$ is the initial value and $b$ is the growth or decay factor.
- A radical function's domain is determined by requiring the radicand to be nonnegative.
Key notation
- $a(x-h)^2+k$ — Vertex form of a quadratic function
Worked example
- Use the function's structure or a given function value to write an equation for the parameter.
Common mistakes
- A function's vertex value is an output, not an input.
- The base of an exponential model is a ratio of consecutive outputs.
How to recognize it
- The problem gives a nonlinear function with one unknown parameter.
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