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 piecewise definition.

Front

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

Back

DNE stands for 'Does Not Exist', indicating that the function does not have a value at that particular input.

Front

If g(x) = { 2x + 3 for x < 0; x^2 for x >= 0, what is g(-2)?

Back

g(-2) = 2(-2) + 3 = -4 + 3 = -1.

Front

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

Back

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

Front

What is the range of a piecewise function?

Back

The range of a piecewise function is the set of all output values (y-values) that the function can produce, based on the defined pieces.

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 circles to indicate whether endpoints are included.

Front

What is the importance of continuity in piecewise functions?

Back

Continuity in piecewise functions ensures that there are no breaks or jumps in the graph, which is important for certain applications in calculus and real-world modeling.

Front

What is a common mistake when working with piecewise functions?

Back

A common mistake is to use the wrong piece of the function for a given input, often due to misreading the intervals.