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 then use the corresponding expression to find the function value.

Front

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

Back

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

Front

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

Back

f(-1) = -1 + 2 = 1.

Front

If g(x) = { -x for x < 0; 2x for x >= 0, what is g(4)?

Back

g(4) = 2(4) = 8.

Front

What is the importance of the domain in piecewise functions?

Back

The domain specifies the intervals over which each piece of the function is applicable, which is crucial for evaluating the function correctly.

Front

How can 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 dots as appropriate for endpoints.

Front

What is the value of f(0) if f(x) = { 3 for x < 0; 5 for x >= 0?

Back

f(0) = 5, since 0 falls into the second interval.

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

How do you find the limit of a piecewise function at a point?

Back

To find the limit, evaluate the left-hand limit and right-hand limit at that point and check if they are equal.