Revision sheet

Function families

Base or exponent, denominator, log, periodic: each family has its sign.

Watch out: x in the exponent means exponential, not polynomial.

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.

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.

Vertex form

$y = a(x - h)^2 + k$: vertex $(h, k)$.

Watch out: $(x + h)$ means the vertex is at $-h$.

Linear or exponential?

Equal differences: linear. Equal factors: exponential.

Watch out: exponential growth wins in the end.

Lines from equations

Intercepts: set the other variable to 0. Slope: solve for $y$.

Watch out: slope of $Ax + By = C$ is $-A/B$.

How many solutions?

Different slopes: one. Parallel: none. Same line: infinitely many.

Watch out: same slope alone is not enough; check the intercepts.

Inequalities in two variables

Dashed for $<, >$; solid for $\le, \ge$. Test a point to choose the side.

Watch out: “at most” is $\le$, “at least” is $\ge$.