Linear and Nonlinear Functions

Front

What is a function?

Back

A function is a relation where each 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

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation y = mx + b.

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, etc.

Tags

CCSS.8.F.A.3

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change, while nonlinear functions have a variable rate of change.

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CCSS.8.F.A.3

Front

What does it mean for a table to represent a function?

Back

A table represents a function if each input value corresponds to exactly one output value.

Tags

CCSS.8.F.A.1

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) that represent a point on a graph.

Tags

CCSS.5.G.A.1

Front

Can a function have the same output for different inputs?

Back

No, a function cannot have the same output for different inputs; each input must map to one unique output.

Tags

CCSS.8.F.A.1

Front

What is the slope of a linear function?

Back

The slope is the ratio of the rise (change in y) to the run (change in x) between two points on the line.

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 (x=0).