ALG1H 4.7 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 parts of its domain.

Front

How do you evaluate a piecewise function?

Back

To evaluate a piecewise function, determine which piece of the function applies to the given input value and then use that expression to find the output.

Front

What does f(2) = 1 indicate in a piecewise function?

Back

It indicates that when the input x is 2, the output of the function f is 1.

Front

If f(x) = { x + 2 for x < 0; x - 1 for x >= 0, what is f(-3)?

Back

f(-3) = -3 + 2 = -1.

Front

What is the domain of a piecewise function?

Back

The domain of a piecewise function is the set of all possible input values (x) for which the function is defined.

Front

What is the range of a piecewise function?

Back

The range of a piecewise function is the set of all possible output values (f(x)) that the function can produce.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function according to its defined interval and connect the points appropriately.

Front

What is the significance of the endpoints in a piecewise function?

Back

Endpoints determine whether the function includes or excludes certain values, affecting the continuity of the graph.

Front

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

Back

f(1) = 3.

Front

What is a continuous piecewise function?

Back

A continuous piecewise function is one where there are no breaks or jumps in the graph, meaning the pieces connect smoothly.