Piecewise Function Review

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different intervals 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 interval the point falls into and use the corresponding expression to find the function's value.

Front

What does 'DNE' stand for in the context of piecewise functions?

Back

DNE stands for 'Does Not Exist', indicating that the function value is not defined for that particular input.

Front

If f(x) = { x^2 for x < 0; 2x + 1 for x >= 0, what is f(-1)?

Back

f(-1) = (-1)^2 = 1.

Front

If f(x) = { 3x - 2 for x < 1; 4 for x = 1; x + 5 for x > 1, what is f(1)?

Back

f(1) = 4.

Front

What is the significance of the 'pieces' in a piecewise function?

Back

The 'pieces' represent different rules or formulas that apply to different sections of the function's domain.

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How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece according to its defined interval, ensuring to use open or closed circles to indicate whether endpoints are included.

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What is the domain of a piecewise function?

Back

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

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What is the range of a piecewise function?

Back

The range of a piecewise function is the set of all possible output values (f(x)) that the function can produce.

Front

How do you determine continuity in a piecewise function?

Back

A piecewise function is continuous if there are no breaks, jumps, or holes in the graph at the points where the pieces meet.