Linear or Non-Linear?

Front

What is a linear function?

Back

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

Front

What is a non-linear function?

Back

A non-linear function is a function that does not create a straight line when graphed. It can have curves, bends, or other shapes, and its rate of change is not constant.

Front

How can you identify a linear function from a graph?

Back

A linear function can be identified by a straight line on the graph. If the graph curves or bends, it is not a linear function.

Front

What does it mean if a graph is not a function?

Back

A graph is not a function if any vertical line drawn through the graph intersects it at more than one point. This violates the definition of a function, which states that each input must have exactly one output.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, represented by 'm' in the equation y = mx + b. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of a function crosses the y-axis. It is represented by 'b' in the equation y = mx + b.

Front

Can a function be both linear and non-linear?

Back

No, a function cannot be both linear and non-linear. A function is classified as either linear or non-linear based on its graph and equation.

Front

What is 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

What is an example of a non-linear function?

Back

An example of a non-linear function is f(x) = x^2, which represents a parabola and is not a straight line.

Front

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

Back

To determine if a table of values represents a linear function, check if the differences between consecutive y-values are constant for equal differences in x-values.