Linear vs Nonlinear Functions Review Flashcard

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 create a straight line when graphed. Its rate of change is not constant.

Front

How can you identify a linear function from its equation?

Back

If the equation can be written in the form y = mx + b, it is linear. If it includes variables multiplied together or raised to a power, it is nonlinear.

Front

What does it mean for a relationship to be linear?

Back

A linear relationship means that the rate of change between the two variables is constant.

Front

What is the slope of a linear function?

Back

The slope (m) of a linear function represents the rate of change of y with respect to x. It indicates how steep the line is.

Front

What is the y-intercept of a linear function?

Back

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

Front

What is an example of a linear equation?

Back

An example of a linear equation is y = 2x + 3.

Front

What is an example of a nonlinear equation?

Back

An example of a nonlinear equation is y = x^2 + 1.

Front

How can you determine if a table of values represents a linear relationship?

Back

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

Front

What is the significance of a constant rate of change in a linear function?

Back

A constant rate of change means that for every unit increase in x, y increases by a fixed amount.