Linear vs 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.

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 determine if a function is linear from a table of values?

Back

A function is linear if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Tags

CCSS.HSF-LE.A.1B

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output (y-value) for each input (x-value).

Tags

CCSS.8.F.A.1

Front

What does it mean for a relation to not be a function?

Back

A relation is not a function if at least one x-value is associated with more than one y-value.

Tags

CCSS.8.F.A.1

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of a linear function?

Back

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

Front

How can you identify a nonlinear function from its graph?

Back

A nonlinear function can be identified by its curved graph, which does not form a straight line.

Tags

CCSS.8.F.A.3

Front

What is a common example of a nonlinear function?

Back

A common example of a nonlinear function is a quadratic function, which can be represented by the equation f(x) = ax^2 + bx + c.

Front

What is the difference between a linear equation and a linear function?

Back

A linear equation is an equation that represents a straight line, while a linear function is a specific type of linear equation that defines a relationship between x and y.

Tags

CCSS.8.F.A.3