8.F.3 Review - Linear vs. Nonlinear

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed. It can have curves, bends, or changes in direction.

Front

Identify the linear function from the following: y = x^2, f(x) = x^3 + 5, y = 3x + 4, y = 7x^-2 + x + 14.

Back

y = 3x + 4

Front

Identify the nonlinear function from the following: y = 2x^3 - x^2 + 5, y = 5x - 19, 14x - 8 = 2y, 3y = 6x + 15.

Back

y = 2x^3 - x^2 + 5

Front

What does it mean for a function to have a constant rate of change?

Back

A function has a constant rate of change if the difference in y-values divided by the difference in x-values is the same for any two points on the line, characteristic of linear functions.

Front

What is the slope of the linear function y = 3x + 4?

Back

The slope (m) is 3.

Front

What is the y-intercept of the linear function y = 3x + 4?

Back

The y-intercept (b) is 4.

Front

How can you determine if a function is linear from a table of values?

Back

If the differences between consecutive y-values divided by the differences between consecutive x-values are constant, the function is linear.

Front

Why is the function y = x^2 considered nonlinear?

Back

This function is nonlinear because the x-term is raised to the second power, which means it does not have a constant rate of change.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.