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 the input variable.

Front

How do you evaluate a piecewise function at a specific point?

Back

To evaluate a piecewise function at a specific point, identify which interval the input value falls into and use the corresponding expression to find the output.

Front

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

Back

DNE stands for 'Does Not Exist', indicating that there is no output for a given input in the function.

Front

If f(x) = -3, how do you find x?

Back

To find x when f(x) = -3, look for the input values in the piecewise function that yield an output of -3.

Front

What is the output of f(-4) if f(x) is defined as 7 for x < -4?

Back

The output of f(-4) is 7, as it falls within the defined interval.

Front

What is the significance of the domain in piecewise functions?

Back

The domain of a piecewise function specifies the input values for which the function is defined, often divided into intervals.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece according to its defined interval and connect the points appropriately.

Front

What is the output of f(-5) if f(x) is defined as 0 for x < -4?

Back

The output of f(-5) is 0, as it falls within the defined interval.

Front

What does it mean if a piecewise function has a jump discontinuity?

Back

A jump discontinuity occurs when the function has different values at the same point from the left and right sides.

Front

How do you determine if a piecewise function is continuous?

Back

A piecewise function is continuous if there are no jumps, breaks, or holes in the graph at the boundaries of the intervals.