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 domain of a piecewise function?

Back

The domain of a piecewise function is the set of all input values (x-values) for which the function is defined, often specified by the intervals in the function's definition.

Front

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

Back

f(x) represents the output of the function for a given input x, which can vary depending on the piecewise definition.

Front

If f(x) = -x + 4 for x < 2, what is f(1)?

Back

f(1) = -1 + 4 = 3.

Front

If f(x) = 2x - 6 for x >= 2, what is f(3)?

Back

f(3) = 2(3) - 6 = 0.

Front

What is the significance of the point where the pieces of a piecewise function meet?

Back

The point where the pieces meet is called a breakpoint, and it is important for determining the continuity 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 value of f(0) if f(x) = -3 for x < 0 and f(x) = 4 for x >= 0?

Back

f(0) = 4.

Front

What is the value of g(4) if g(x) = -5 for x < 4 and g(x) = 13 for x >= 4?

Back

g(4) = 13.