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 determine the value of a piecewise function at a specific point?

Back

To determine the value of a piecewise function at a specific point, identify which interval the point falls into and 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 is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph.

Front

What is the difference between open and closed intervals?

Back

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

Front

How do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function according to its defined interval, ensuring to use open or closed dots as appropriate.

Front

What is the significance of the 'greater than' and 'less than' symbols in piecewise functions?

Back

They determine whether the endpoints of the intervals are included in the domain of the function.

Front

What is a common mistake when working with piecewise functions?

Back

A common mistake is to incorrectly apply the function's definition at the boundaries of the intervals.

Front

How do you find the intersection of two piecewise functions?

Back

To find the intersection, set the two functions equal to each other and solve for x within the defined intervals.