• $f(x)$
• Domain and Range
• Vertical line test, each input has one output.

Classification

Even functions: $f(x)=f(-x)$ Odd functions: $f(x)=-f(-x)$

one to many, many to many, many to one. onto: every $y$ can be mapped onto.

Inverse Functions

$f^{-1}(f(x))=x$. To get it, swap $y$ and $x$.

Quadratics

$y=a{x}^2+bx+c$ $y=a(x-h{)}^2+d$ Quadratic formula is cool.

Rational functions

$\frac{1}{x}$

• Vertical asymptotes at denominator = 0
• Horizontal asymptotes ${\lim }_{x\to \infty }f(x)$

Radicals

About the same, just $\sqrt{f(x)}$

Absolute Value Equations

In the form of $y=|x|$, solve it with $y=\pm x$.

Inequalities

Solve by finding the ranges of positive and negative between zeros.

Transformation

Biggest and most important summary of the entire chapter: $y=af(b(x-h))+k$ Dilations, reflections, translations of graphs, and $\frac{1}{f(x)}$ takes all $x$-intercepts and turns them into asymptotes.

Logarithms

Two important log rules: ${\log }_a(b^x)=x{\log }_a(b)$ and change in bases: ${\log }_{a}b=\frac{{\log }_{c}b}{{\log }_{c}a}$