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

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 if a piecewise function has a domain restriction?

Back

A domain restriction means that the function is only defined for certain values of x, excluding others.

Front

Evaluate f(-5) for the piecewise function: f(x) = { 0 if x < 0, 2 if 0 ≤ x < 5, 5 if x ≥ 5 }

Back

0

Front

What is the domain restriction of the blue piece of this function if it is defined as: f(x) = { x^2 if x < 0, 3x if x ≥ 0 }?

Back

x ≥ 0

Front

A house painter charges $12 per hour for the first 40 hours, $18 for the next 10 hours, and $24 for hours beyond that. How much does he earn for a 70 hour week?

Back

$1140

Front

Evaluate g(7) for the piecewise function: g(x) = { -x + 3 if x < 5, 2x - 1 if x ≥ 5 }

Back

17

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.

Front

What is the difference between an open interval and a closed interval in the context of piecewise functions?

Back

An open interval does not include its endpoints, while a closed interval includes its endpoints.