Linear and Nonlinear Functions

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. Its rate of change is not constant.

Front

What does the slope of a linear function represent?

Back

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

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0, represented by the term 'b' in the equation y = mx + b.

Front

What is the Vertical Line Test?

Back

The Vertical Line Test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

How do you find the rate of change from a table of values?

Back

To find the rate of change, calculate the difference in y-values divided by the difference in x-values between two points.

Front

What is the initial value in the equation y = 8x + 6?

Back

The initial value is 6, which is the y-intercept of the function.

Front

Which of the following represents a linear function: y = 2x + 3 or y = x^2 + 1?

Back

y = 2x + 3 is a linear function; y = x^2 + 1 is a nonlinear function.

Front

What does it mean if a function is increasing?

Back

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

Front

What does it mean if a function is decreasing?

Back

A function is decreasing if, as x increases, y decreases.