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 f(x) = 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 other shapes, and does not have a constant rate of change.

Front

What does it mean for a relation to be 'Not a Function'?

Back

A relation is 'not a function' if it does not pass the vertical line test, meaning that for at least one input, there are multiple outputs.

Front

Give an example of a Linear Function.

Back

An example of a linear function is f(x) = 2x + 3, which represents a straight line with a slope of 2 and a y-intercept of 3.

Front

Give an example of a Nonlinear Function.

Back

An example of a nonlinear function is f(x) = x^2, which represents a parabola that opens upwards.

Front

What is the slope in a linear function?

Back

The slope (m) in a linear function 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 in a linear function?

Back

The y-intercept (b) in a linear function is the point where the line crosses the y-axis, representing the value of f(x) when x = 0.

Front

How can you identify a Linear Function from a table of values?

Back

A linear function will have a constant difference in the y-values for equal intervals in the x-values.

Front

How can you identify a Nonlinear Function from a table of values?

Back

A nonlinear function will show varying differences in the y-values for equal intervals in the x-values.

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.