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.

Front

What does the domain of a function represent?

Back

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

Front

How do you determine the domain of a piecewise function?

Back

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

Front

What is the significance of the notation 'x ≥ 0'?

Back

The notation 'x ≥ 0' indicates that x can take any value greater than or equal to 0.

Front

What does the interval '-2 < x ≤ 1' mean?

Back

The interval '-2 < x ≤ 1' means that x can take any value greater than -2 and up to and including 1.

Front

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 use the corresponding expression.

Front

What is the output of f(0) if f(x) = { 0 for x < 0; 19 for x = 0; 9 for x > 0 }?

Back

The output of f(0) is 19.

Front

What is the output of f(-3) if f(x) = { -3 for x < -2; -1 for -2 ≤ x < 0; 1 for x ≥ 0 }?

Back

The output of f(-3) is -3.

Front

What is a graph of a piecewise function?

Back

A graph of a piecewise function consists of multiple segments, each representing a different expression of the function over specific intervals.

Front

What is the importance of understanding domain restrictions in piecewise functions?

Back

Understanding domain restrictions helps in determining where the function is valid and aids in graphing the function accurately.