Functions, Domain, and Range

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Tags

CCSS.8.F.A.1

Front

What is the domain of a function?

Back

The domain of a function is the complete set of possible values of the independent variable (input) for which the function is defined.

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What is the range of a function?

Back

The range of a function is the complete set of possible values of the dependent variable (output) that the function can produce.

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How do you determine the domain of a function?

Back

To determine the domain, identify all the values of the independent variable that do not cause the function to be undefined (e.g., avoid division by zero or taking the square root of a negative number).

Front

How do you determine the range of a function?

Back

To determine the range, evaluate the function for all values in the domain and identify all possible output values.

Front

What does it mean for a function to be positive?

Back

A function is positive when its output values are greater than zero for the values in its domain.

Tags

CCSS.HSF.LE.B.5

Front

What is a linear function?

Back

Tags

CCSS.HSF.LE.A.2

CCSS.8.F.B.4

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed, meaning it can have curves, bends, or other shapes.

Tags

CCSS.8.F.A.3

Front

What is the vertical line test?

Back

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

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output value is associated with exactly one input value, meaning no two different inputs produce the same output.