AP Precalculus Function Features

A positive rate of change indicates that the function's output is…

• Decreasing

• Constant

• Increasing

• Fluctuating

A relative minimum occurs when a function f...

• changes from increasing to decreasing.

• remains constant over an interval.

• changes from decreasing to increasing.

• increases at an increasing rate.

The slope of a function at any given point gives…

• The maximum value of the function at that point.

• The rate of change of the function at that input.

• The y-intercept of the function.

• The average value of the function over an interval.

A relative maximum occurs when a function f changes from increasing to decreasing.

• Changes from increasing to decreasing.

• Changes from decreasing to increasing.

• Remains constant over an interval.

• Increases indefinitely without bound.

One-to-one function

• A function where each input has a unique output (no repeated outputs).

• A function that can have multiple outputs for a single input.

• A function that is defined for all real numbers.

• A function that is always increasing or decreasing.

A function f is decreasing on an interval if...

• As the input values increase, the output values always decrease.

• The function has a positive slope throughout the interval.

• For all a and b in the interval, if a > b, then f(a) < f(b).

• The function is constant on the interval.

A function is exponential if, as input values change ____, output values change ____.

• additively

• linearly

• quadratically

• multiplicatively

A function f is increasing on an interval if…

• As the input values increase, the output values always increase.

• The output values decrease as the input values increase.

• For all a and b in the interval, if a > b, then f(a) > f(b).

• The function has a constant output regardless of the input.

A function is linear if, over equal-length input intervals, output values

• change by a constant amount.

• change by a variable amount.

• are always zero.

• increase exponentially.

A function f is concave down if…

• The rates of change of f are increasing.

• The rates of change of f are constant.

• The rates of change of f are decreasing.

• The rates of change of f are oscillating.