Linear 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 for different parts of its domain.

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How do you evaluate a piecewise function at a specific point?

Back

To evaluate a piecewise function at a specific point, determine which piece of the function applies to that point and then use the corresponding expression to find the value.

Front

What is the domain of a function?

Back

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

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What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph.

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What is the range of a function?

Back

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

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How do you find the value of f(x) for a piecewise function?

Back

To find f(x), identify the interval in which x falls and use the corresponding expression for that interval.

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What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

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What is the slope of a line?

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The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

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What does 'f(-2) = 8' indicate in a piecewise function?

Back

It indicates that when x = -2, the output of the function f is 8, based on the specific piece of the function that applies at that point.

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What are domain restrictions in piecewise functions?

Back

Domain restrictions specify the values of x for which a particular piece of the function is valid.