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 intervals 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 interval the point falls into and then use the corresponding expression to find the function's value.

Front

What does 'undefined' mean in the context of piecewise functions?

Back

'Undefined' means that there is no valid output for the given input, often because the input does not fall within any defined interval of the piecewise function.

Front

If a piecewise function is defined as f(x) = { x^2 for x < 0, 2x + 1 for x >= 0, what is f(-2)?

Back

f(-2) = (-2)^2 = 4.

Front

If a piecewise function is defined as f(x) = { 3x + 2 for x < 1, 5 for x = 1, 2x - 1 for x > 1, what is f(1)?

Back

f(1) = 5.

Front

What is the significance of the domain in piecewise functions?

Back

The domain of a piecewise function specifies the intervals for which each piece of the function is applicable.

Front

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.

Front

What is the output of a piecewise function if the input is outside its defined intervals?

Back

The output is typically 'undefined' if the input does not fall within any of the defined intervals.

Front

If a dog weighs 15 pounds and the cost is defined as { $35 for 0 < weight <= 20, $40 for 21 < weight <= 40, what is the cost?

Back

The cost is $35.

Front

Evaluate the piecewise function f(x) = { -1 for x < 0, 4 for x = 0, x^2 - 1 for x > 0 at x = 0.

Back

f(0) = 4.