Advanced Math / Nonlinear Functions
Nonlinear Functions
Nonlinear functions include quadratic, exponential, polynomial, radical, and rational functions. SAT-style questions often ask for function values, intercepts, maximum or minimum values, vertex information, transformations, domain restrictions, or the meaning of parameters in context.
Least you need to know
- For $f(x)=a(x-h)^2+k$, the vertex is $(h,k)$.
- For an exponential function $f(x)=ab^x$, $a$ is the initial value and $b$ is the growth or decay factor.
Key notation
- $f(x)$ — The output of function $f$ for input $x$
Worked example
- Evaluate the function or use its structure to identify key features.
Common mistakes
- In vertex form, $x-h$ gives vertex x-coordinate $h$.
- For exponential decay, the factor is between 0 and 1.
How to recognize it
- The function includes powers, roots, exponentials, or a variable in a denominator.
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