Revision sheet

Domain and range

• Domain: the inputs. Leave out zero denominators and negatives under a square root.
• Range: the outputs.
• $[a, \infty)$ includes $a$; $(a, \infty)$ does not.

Watch out: the range uses $y$-values, not the $x$ of a vertex.

Average rate of change

• From $a$ to $b$: $\dfrac{f(b) - f(a)}{b - a}$, output change over input change.
• Increasing: the graph rises from left to right.
• Give intervals of increase with $x$-values.

Watch out: change in $f(x)$ on top, change in $x$ below.

Linear or exponential?

Equal differences: linear. Equal factors: exponential.

Watch out: exponential growth wins in the end.

Writing an exponential function

• $f(x) = a \cdot b^x$: $a = f(0)$, $b = \dfrac{f(1)}{f(0)}$.
• Multiplied by $b$ every $n$ units: $f(x) = a \cdot b^{\frac{x}{n}}$.

Watch out: the starting value is $f(0)$, and it goes in front, not in the base.