A 1.4 Attributes of Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

Front

Define increasing function.

Back

An increasing function is one where, as the input values increase, the output values also increase.

Front

Define decreasing function.

Back

A decreasing function is one where, as the input values increase, the output values decrease.

Front

What is a local minimum?

Back

A local minimum is a point on the graph of a function where the function value is lower than all nearby points.

Front

What is an interval of increase?

Back

An interval of increase is a range of x-values over which the function's output values are increasing.

Front

What is an interval of decrease?

Back

An interval of decrease is a range of x-values over which the function's output values are decreasing.

Front

How do you identify intervals of increase and decrease from a graph?

Back

Intervals of increase are where the graph rises from left to right, and intervals of decrease are where the graph falls.

Front

What does it mean for a function to be constant?

Back

A constant function has the same output value for every input value, resulting in a horizontal line on the graph.

Front

What is the significance of critical points?

Back

Critical points are where the derivative is zero or undefined, indicating potential local maxima, minima, or points of inflection.

Front

How do you find the local maximum of a function?

Back

A local maximum occurs at a critical point where the function changes from increasing to decreasing.