3.2 Linear vs. Nonlinear

Front

What is a linear equation?

Back

An equation that forms a straight line when graphed, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear equation?

Back

An equation that does not form a straight line when graphed, which can include curves, circles, or other shapes.

Front

What does it mean for a function to be continuous?

Back

A function is continuous if its graph can be drawn without lifting the pencil from the paper, meaning there are no breaks or holes.

Front

What does it mean for a function to be discrete?

Back

A function is discrete if it consists of distinct, separate values, often represented as individual points on a graph.

Front

How can you identify a linear function from its graph?

Back

A linear function will have a graph that is a straight line.

Front

How can you identify a nonlinear function from its graph?

Back

A nonlinear function will have a graph that is not a straight line, showing curves or bends.

Front

What are x-values in the context of a function?

Back

X-values are the input values of a function, representing the independent variable.

Front

What are y-values in the context of a function?

Back

Y-values are the output values of a function, representing the dependent variable.

Front

What is the slope in a linear equation?

Back

The slope (m) represents the rate of change of the function, indicating how steep the line is.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis, indicating the value of y when x is 0.