AP PRE CALC 1.1 -1.4 study guide

Function

Each input has exactly one output.

Domain

All possible inputs of a function.

Range

All possible outputs of a function.

Rate of Change

Slope of a function; indicates how output changes with input.

Positive Rate of Change

Indicates a positive slope and that the function is increasing.

Negative Rate of Change

Indicates a negative slope and that the function is decreasing.

Zero Rate of Change

Indicates horizontal slope at that point.

Linear Function

Function with a constant rate of change.

Quadratic Function

Function that forms a parabola; has a variable rate of change.

Concave Up

Function where slopes are getting more positive or less negative.

Concave Down

Function where slopes are getting more negative or less positive.

Relative Maximum

Point where the function changes from increasing to decreasing.

Relative Minimum

Point where the function changes from decreasing to increasing.

Point of Inflection

Point where the graph changes concavity.

Average Rate of Change (AROC)

Formula for average rate of change: $\frac{f(b)-f(a)}{b-a}$.

Leading Coefficient

Coefficient of the term with the largest exponent.

Polynomial Degree

The largest exponent of a polynomial.

Positive Function

Function values above the x-axis.

Negative Function

Function values below the x-axis.

Increasing Function

Function where graph goes up from left to right.

Decreasing Function

Function where graph goes down from left to right.