Linear vs NonLinear Functions

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What is a linear function?

Back

A linear function is a function that graphs to a straight line. It 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. Its graph can be a curve, a circle, or any other shape that is not a straight line.

Tags

CCSS.8.F.A.3

Front

How can you tell if a table represents a function?

Back

A table represents a function if each input (x-value) corresponds to exactly one output (y-value). If an x-value is repeated with different y-values, it is not a function.

Tags

CCSS.8.F.A.1

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis. It is the value of y when x = 0.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input is associated with exactly one output. A relation can have multiple outputs for a single input.

Tags

CCSS.8.F.A.1

Front

What are some examples of nonlinear functions?

Back

Examples of nonlinear functions include quadratic functions (e.g., y = x^2), exponential functions (e.g., y = 2^x), and trigonometric functions (e.g., y = sin(x)).

Tags

CCSS.8.F.A.3

Front

What does it mean for a graph to be nonlinear?

Back

A graph is nonlinear if it does not form a straight line. This can include curves, circles, or any other shape that deviates from linearity.

Tags

CCSS.8.F.A.3

Front

How can you identify a linear function from a graph?

Back

A linear function can be identified from a graph if it forms a straight line, has a constant slope, and passes the vertical line test.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.