ALG1H 4.7 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 to find the value.

Front

What does f(0) = 4 indicate in a piecewise function?

Back

It indicates that when the input (x) is 0, the output (f(0)) is 4, based on the definition of the function at that point.

Front

If f(2) = 1, what does this tell us about the function at x = 2?

Back

It tells us that when the input (x) is 2, the output (f(2)) is 1, indicating the value of the function at that specific point.

Front

What is the significance of finding f(-2) = 8 in a piecewise function?

Back

It shows that for the input (x) of -2, the output (f(-2)) is 8, which is determined by the relevant piece of the function.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function according to its defined interval and ensure to use open or closed circles to indicate whether endpoints are included.

Front

What is the domain of a piecewise function?

Back

The domain of a piecewise function is the set of all possible input values (x) for which the function is defined, which may vary across different pieces.

Front

What is the range of a piecewise function?

Back

The range of a piecewise function is the set of all possible output values (f(x)) that the function can produce, depending on the defined pieces.

Front

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

Back

A discontinuity in a piecewise function means there is a break or jump in the graph, indicating that the function is not continuous at that point.

Front

How do you determine if a piecewise function is continuous at a point?

Back

A piecewise function is continuous at a point if the limit from the left equals the limit from the right and both equal the function's value at that point.