Linear Vs. Nonlinear (Tables, Equations, Graphs)

Front

What is a linear function?

Back

A linear function is a function that has a constant rate of change, which means that the graph of the function forms a straight line.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not have a constant rate of change, resulting in a graph that is not a straight line.

Front

What does the y-intercept represent in a linear function?

Back

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

Front

How can you identify a linear function from a table of values?

Back

A linear function can be identified from a table if the ratio of the change in the y values to the change in the x values is constant.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in the y value to the change in the x value, representing the steepness of the line.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which forms a parabolic curve.

Front

What does it mean if a function has an exponent?

Back

If a function has an exponent greater than 1, it is typically nonlinear because the rate of change is not constant.

Front

How can you tell if a graph is linear or nonlinear?

Back

A graph is linear if it forms a straight line; it is nonlinear if it curves or has any bends.

Front

What is the significance of a constant rate of change?

Back

A constant rate of change indicates that for every unit increase in x, the y value increases by a fixed amount, characteristic of linear functions.

Front

What is a common characteristic of nonlinear functions?

Back

Nonlinear functions often have varying rates of change, which can result in curves, bends, or other complex shapes in their graphs.