Piecewise Functions

Front

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.

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.

Front

What does it mean for a function to be defined at a point?

Back

A function is defined at a point if there is a corresponding output value (y-value) for that input value (x-value).

Front

What is the range of a piecewise function?

Back

The range of a piecewise 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(-1) for a piecewise function?

Back

Identify which piece of the function applies when x = -1, then substitute -1 into that expression.

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What is the significance of the inequality in piecewise functions?

Back

Inequalities in piecewise functions determine the intervals over which each piece of the function is valid.

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How do you graph a piecewise function?

Back

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

Front

What does 'DNE' stand for in function evaluation?

Back

DNE stands for 'Does Not Exist', indicating that the function does not have a value at that specific input.

Front

What is the formula for the piecewise function: 4-x for x<2 and 2x-6 for x≥2?

Back

The piecewise function is defined as: f(x) = { 4-x, x<2; 2x-6, x≥2 }.