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, determine which interval the input value falls into and then use the corresponding expression to find the output.

Front

What does the notation f(x) mean in a piecewise function?

Back

f(x) represents the output of the function for a given input x.

Front

What is the significance of the domain in piecewise functions?

Back

The domain specifies the set of 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 of the function on its respective interval, ensuring to use open or closed dots based on whether the endpoints are included.

Front

What is the value of f(0) if f(x) = { 0.5x + 2.5 for x < 0, 4 for x = 0, 0.5x + 2 for x > 0 }?

Back

f(0) = 4.

Front

What is the output of the function m(x) = { -3 for x < -2, 0.5 for -2 ≤ x < 1, 3 for x ≥ 1 } at x = -3?

Back

m(-3) = -3.

Front

What is the output of the function g(x) = { -17 for x < 0, 13 for 0 ≤ x < 10, 17 for x ≥ 10 } at x = 7?

Back

g(7) = 13.

Front

What is the slope of the line represented by the expression 0.5x + 2.5?

Back

The slope is 0.5.

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.