Linear vs. Nonlinear functions

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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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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, and it can take various forms such as quadratic, exponential, or logarithmic.

Tags

CCSS.8.F.A.3

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change between the x-values and y-values. If the differences in y-values divided by the differences in x-values are the same for all pairs, the function is linear.

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CCSS.HSF-LE.A.1B

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 f(x) = mx + b. It is calculated as the change in y divided by the change in x.

Tags

CCSS.8.EE.B.5

Front

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

Back

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

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.

Front

What is an example of a nonlinear function?

Back

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

Tags

CCSS.8.F.A.3

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value). A relation can have multiple outputs for a single input.

Tags

CCSS.8.F.A.1

Front

What ordered pairs can prevent a table from being a function?

Back

Ordered pairs that have the same x-value but different y-values prevent a table from being a function.

Tags

CCSS.8.F.A.1

Front

How can you graph a linear function?

Back

To graph a linear function, plot the y-intercept on the y-axis, use the slope to find another point, and draw a straight line through the points.

Tags

CCSS.HSF-IF.C.7A