Piecewise Functions

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What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas over different intervals of its domain.

Tags

CCSS.HSF-IF.C.7B

Front

How do you determine the domain of a piecewise function?

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To determine the domain, identify the intervals for which each piece of the function is defined and combine them.

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What is the range of a function?

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The range of a function is the set of all possible output values (y-values) that the function can produce.

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What does it mean for a function to behave like a quadratic function?

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A function behaves like a quadratic function if it can be represented by a polynomial of degree 2, typically having a parabolic shape.

Front

How do you find the range of a piecewise function?

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To find the range, evaluate each piece of the function over its domain and combine the resulting output values.

Front

What is the significance of domain restrictions in piecewise functions?

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Domain restrictions indicate the values of x for which the function is defined, helping to avoid undefined expressions.

Tags

CCSS.HSF-IF.C.7B

Front

What is the difference between open and closed intervals?

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Open intervals do not include their endpoints (e.g., (a, b)), while closed intervals do include their endpoints (e.g., [a, b]).

Tags

CCSS.6.EE.B.8

Front

How can you graph a piecewise function?

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To graph a piecewise function, plot each piece of the function on its respective interval, ensuring to use open or closed dots as needed.

Tags

CCSS.HSF-IF.C.7B

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What is an example of a piecewise function?

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An example is: f(x) = { x^2 for x < 0, 2x + 1 for x ≥ 0 }.

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What does the notation f(x) = { ... } signify?

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This notation signifies that the function f(x) is defined by multiple expressions based on the value of x.