Evaluating 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 use the corresponding expression to find the function's value.

Front

What is the value of m(-3) if m(x) = { 3 for x < -2; 0 for -2 ≤ x < 2; -3 for x ≥ 2 }?

Back

3

Front

What is the value of f(-3) if f(x) = { 6 for x < -1; -4 for -1 ≤ x < 0; 2 for x ≥ 0 }?

Back

6

Front

What is m(4) if m(x) = { -3 for x < 0; 0 for 0 ≤ x < 5; 2 for x ≥ 5 }?

Back

0

Front

Find f(2) if f(x) = { 0 for x < 1; 1 for 1 ≤ x < 3; 4 for x ≥ 3 }.

Back

f(2) = 1

Front

What is f(1) if f(x) = { 6 for x < 0; -2 for 0 ≤ x < 2; sqrt(2) for x ≥ 2 }?

Back

-2

Front

What does it mean for a piecewise function to be continuous?

Back

A piecewise function is continuous if there are no breaks, jumps, or holes in the graph at the points where the pieces meet.

Front

How can 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 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-values) for which the function is defined.