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?

Back

To evaluate a piecewise function, identify the interval that contains the input value and use the corresponding expression to find the output.

Front

What does f(0) represent in a function?

Back

f(0) represents the value of the function when the input x is 0.

Front

If f(x) = { 2x + 1 for x < 0; 3 for x = 0; x - 1 for x > 0 }, what is f(0)?

Back

f(0) = 3.

Front

What is the value of f(6) if f(x) = { x^2 - 10 for x < 5; 2x + 1 for x >= 5 }?

Back

f(6) = 2(6) + 1 = 13.

Front

What is the significance of the domain in piecewise functions?

Back

The domain specifies the input values for which the function is defined, and it can vary for different pieces of the function.

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 output of f(-3) if f(x) = { -x for x < 0; x^2 for x >= 0 }?

Back

f(-3) = -(-3) = 3.

Front

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

Back

A jump discontinuity occurs when the left-hand limit and right-hand limit at a point do not equal each other, resulting in a 'jump' in the graph.

Front

If f(x) = { x + 2 for x < 1; 3 for x = 1; x^2 for x > 1 }, what is f(1)?

Back

f(1) = 3.