Flashcard 9

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in 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 graph to a straight line. Its rate of change varies, and it can be represented by equations such as quadratics, cubics, etc.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x = 0.

Front

How can you identify a linear function from an equation?

Back

If the equation can be written in the form y = mx + b, it is linear. If it includes variables raised to powers greater than one, it is nonlinear.

Front

What is the equation of a linear function?

Back

The general form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which represents a parabola.

Front

How do you determine if a table of values represents a linear function?

Back

If the differences between consecutive y-values are constant for equal intervals of x, the function is linear.

Front

What is the difference between a linear and a nonlinear graph?

Back

A linear graph is a straight line, while a nonlinear graph can be curved or have varying slopes.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as x increases, y also increases.