Revision sheet

Functions

Exactly one output for each input.

Watch out: shared outputs are fine; two outputs for one input are not.

Function notation

• $f(a)$ is the output for the input $a$.
• Replace every $x$ by $(a)$, with parentheses: $f(-2)$ for $x^2$ is $(-2)^2 = 4$.
• On a graph: the height above $x = a$.

Watch out: $f(a + b)$ is not $f(a) + f(b)$.

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.

Prisms and cylinders

$V = Bh$; cylinder $V = \pi r^2 h$.

Watch out: base area, not circumference.

Pyramids and cones

$V = \tfrac{1}{3}Bh$.

Watch out: do not forget the ⅓.

Spheres and density

$V = \tfrac{4}{3}\pi r^3$; density = mass/volume.

Watch out: $r^3$ for volume, $r^2$ for area.