8.6.5 HOMEWORK - Increasing and Decreasing Functions

Front

What is a function in mathematics?

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

How can you determine if a set of coordinates represents a function?

Back

A set of coordinates represents a function if no two different ordered pairs have the same first element (x-value).

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, for any two points in that interval, the function's value at the second point is greater than the value at the first point.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, for any two points in that interval, the function's value at the second point is less than the value at the first point.

Front

How can you identify the intervals where a function is increasing or decreasing from a graph?

Back

You can identify increasing intervals where the graph rises from left to right and decreasing intervals where the graph falls from left to right.

Front

What is the significance of the x-axis in determining increasing and decreasing functions?

Back

The x-axis helps to identify the intervals of increase or decrease by showing where the function's output values (y-values) rise or fall as x-values change.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a graph of a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the definition of a graph of a function?

Back

A graph of a function is a visual representation of the relationship between the input (x-values) and output (y-values) of the function.

Front

What are the characteristics of a function that is constant?

Back

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

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input is associated with exactly one output, while a relation can have multiple outputs for a single input.