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 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 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

How can you determine the value of f(-3) from a graph?

Back

To find f(-3), locate -3 on the x-axis and see where the graph intersects the vertical line at x = -3.

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 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 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.

Front

What is the significance of the notation f(x) in piecewise functions?

Back

f(x) represents the output of the function for a given input x, and it can change based on the piecewise definition.

Front

How do you graph a piecewise function?

Back

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