math quiz 1 study

When to use parenthesis $($ or $)$ in interval notation

When the endpoint is NOT included.

When to use bracket $[$ or $]$ in interval notation

When the endpoint IS included.

Notation rule for infinity ($\infty$ or $-\infty$) in interval notation

Always use parentheses, never brackets.

Domain of a function

All possible $x$-values.

Range of a function

All possible $y$-values.

Definition and coordinate condition for an $x$-intercept

Where the graph crosses the $x$-axis ($y = 0$).

Definition and coordinate condition for a $y$-intercept

Where the graph crosses the $y$-axis ($x = 0$).

Formula for average rate of change on interval $[a, b]$

$$\frac{f(b) - f(a)}{b - a}$$

How to identify where a graph is increasing

Look for where the graph goes up from left to right.

How to identify where a graph is decreasing

Look for where the graph goes down from left to right.

Maximum of a graph

The highest $y$-value on the graph.

Minimum of a graph

The lowest $y$-value on the graph.

How to evaluate a piecewise function for a given $x$

Use the equation whose condition includes the given $x$-value.

Graph transformation $f(x + h)$

Shifts the graph left $h$ units.

Graph transformation $f(x - h)$

Shifts the graph right $h$ units.

Graph transformation $f(x) + k$

Shifts the graph up $k$ units.

Graph transformation $f(x) - k$

Shifts the graph down $k$ units.

Graph transformation $-f(x)$

Reflects the graph over the $x$-axis.

Condition for vertical stretch in $a \cdot f(x)$

When $a > 1$.

Condition for vertical compression in $a \cdot f(x)$

When $0 < a < 1$.

Boundary meaning of $<$ or $>$ on a graph

Endpoint is NOT included (represented by an open circle).

Boundary meaning of $\le$ or $\ge$ on a graph

Endpoint IS included (represented by a closed circle).