Analyzing Functions & Graphs

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

What does it mean for a graph to be increasing?

Back

A graph is increasing on an interval if, as you move from left to right, the y-values of the function increase.

Front

What does it mean for a graph to be decreasing?

Back

A graph is decreasing on an interval if, as you move from left to right, the y-values of the function decrease.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, which can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a non-linear function?

Back

A non-linear function is a function that does not graph to a straight line, meaning it can curve or have varying slopes.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

What does it mean for an object to be at rest in a graph?

Back

An object is at rest when its position does not change over time, represented by a horizontal line on a graph.

Front

How can you determine the steepness of a graph?

Back

The steepness of a graph can be determined by the slope; a steeper slope indicates a greater rate of change.

Front

What is the y-intercept of a graph?

Back

The y-intercept is the point where the graph crosses the y-axis, indicating the value of y when x is 0.

Front

What is an interval in the context of a graph?

Back

An interval is a range of x-values over which a function is analyzed, often used to determine increasing or decreasing behavior.