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 does 'DNE' stand for in the context of functions?

Back

DNE stands for 'Does Not Exist', indicating that a function value is undefined at a certain point.

Front

How many pieces are in the function f(x) = { x^2 for x < 0, 2x + 1 for x >= 0 }?

Back

There are 2 pieces in this function.

Front

What is the value of f(-2) for the function f(x) = { x^2 for x < 0, 2x + 1 for x >= 0 }?

Back

f(-2) = 4.

Front

What is the value of f(-3) for the function f(x) = { -x + 4 for x < 2, 2x - 6 for x >= 2 }?

Back

f(-3) = 7.

Front

How do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece according to its defined interval, ensuring to use open or closed circles to indicate whether endpoints are included.

Front

What is the significance of the domain in piecewise functions?

Back

The domain of a piecewise function specifies the intervals over which each piece of the function is valid.

Front

What is the value of g(7) if g(x) = { 2x - 3 for x < 5, x + 10 for x >= 5 }?

Back

g(7) = 17.

Front

What is the formula for the piecewise function f(x) = { -x + 4 if x < 2, 2x - 6 if x >= 2 }?

Back

The function is defined as f(x) = -x + 4 for x < 2 and f(x) = 2x - 6 for x >= 2.