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.

Tags

CCSS.HSF-IF.C.7B

Front

How do you evaluate a piecewise function?

Back

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

Tags

CCSS.HSF.IF.A.2

Front

What is a discontinuity in a function?

Back

A discontinuity is a point at which a function is not continuous, meaning there is a break, jump, or hole in the graph of the function.

Tags

CCSS.HSF-IF.C.7D

Front

What are the types of discontinuities?

Back

The main types of discontinuities are removable discontinuity, jump discontinuity, and infinite discontinuity.

Tags

CCSS.HSF-IF.C.7D

Front

What is a removable discontinuity?

Back

A removable discontinuity occurs when a function has a hole at a point, which can be 'removed' by redefining the function at that point.

Tags

CCSS.HSF-IF.C.7D

Front

What is a jump discontinuity?

Back

A jump discontinuity occurs when the left-hand limit and right-hand limit at a point exist but are not equal, causing a 'jump' in the graph.

Tags

CCSS.HSF-IF.C.7D

Front

What is an infinite discontinuity?

Back

An infinite discontinuity occurs when the function approaches infinity or negative infinity as it approaches a certain point.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find the limit of a piecewise function?

Back

To find the limit of a piecewise function at a point, evaluate the left-hand limit and right-hand limit at that point and check if they are equal.

Front

What does it mean for a function to be continuous at a point?

Back

A function is continuous at a point if the limit exists at that point, the function is defined at that point, and the limit equals the function's value.

Front

What is the significance of undefined values in piecewise functions?

Back

Undefined values in piecewise functions indicate points where the function does not have a valid output, often corresponding to discontinuities.

Tags

CCSS.HSF-IF.C.7B