Functions/Linear vs NonLinear Functions

Front

What is a function?

Back

A function is a relation where every input (x-value) has exactly one output (y-value).

Tags

CCSS.8.F.A.1

Front

How can you determine if a graph represents a function?

Back

You can use the 'vertical line test' (or 'pencil test'). If a vertical line intersects the graph at more than one point, it is not a function.

Front

Which of the following sets of values is a function? (9,5) (10,5) (9,-5) (10,-5), (3,4) (4,-3) (7,4) (3, 8), (6,-5) (7, -3) (8, -1) (9, 1), (2, -2) (5, 9) (5, -7) (1, 4)

Back

(6,-5) (7, -3) (8, -1) (9, 1) is a function because each x-value is unique.

Tags

CCSS.8.F.A.1

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = 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 graph to a straight line and can include curves, parabolas, and other shapes.

Tags

CCSS.8.F.A.3

Front

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function; it indicates how much y changes for a unit change in x.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of a function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis (where x = 0).

Front

What is the domain of a function?

Back

The domain is the set of all possible input values (x-values) for the function.

Front

What is the range of a function?

Back

The range is the set of all possible output values (y-values) for the function.

Front

What is the difference between discrete and continuous functions?

Back

Discrete functions have distinct, separate values (like points), while continuous functions have values that form a continuous line or curve.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5