Linear vs Non-Linear 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 non-linear function?

Back

A non-linear function is a function that does not form a straight line when graphed. Its graph can be a curve, a circle, or any other shape that is not a straight line.

Front

What is the general form of a linear equation?

Back

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

Front

What does the slope (m) represent in a linear function?

Back

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

Front

What does the y-intercept (b) represent in a linear function?

Back

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

Front

How can you determine if a relation is a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This can be checked using the vertical line test.

Front

What is the vertical line test?

Back

The vertical line test states that if a vertical line intersects a graph at more than one point, then the graph does not represent a function.

Front

Is the equation y = 2x + 3 a linear function?

Back

Yes, y = 2x + 3 is a linear function because it can be expressed in the form y = mx + b.

Front

Is the equation y = x^2 a linear function?

Back

No, y = x^2 is a non-linear function because it forms a parabola when graphed.

Front

What is an example of a non-linear function?

Back

An example of a non-linear function is y = x^2 or y = sin(x). Both do not form straight lines when graphed.