Key Features of Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

Define the domain of a function.

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

Define the range of a function.

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What does it mean for a function to be positive?

Back

A function is positive on an interval if its output values (y-values) are greater than zero for all inputs in that interval.

Front

What does it mean for a function to be negative?

Back

A function is negative on an interval if its output values (y-values) are less than zero for all inputs in that interval.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as the input values increase, the output values also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as the input values increase, the output values decrease.

Front

How do you find the intervals where a function is positive or negative?

Back

To find the intervals where a function is positive or negative, analyze the sign of the function's output over its domain, often using a sign chart.

Front

What is the significance of critical points in a function?

Back

Critical points are where the function's derivative is zero or undefined; they help identify intervals of increase or decrease.

Front

What is a sign chart?

Back

A sign chart is a visual tool used to determine where a function is positive or negative by testing intervals around critical points.