4A Piecewise and Absolute Value Function

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

Define the domain of a function.

Back

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

Front

Define the range of a function.

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is an absolute value function?

Back

An absolute value function is a function that outputs the distance of a number from zero, regardless of direction, typically written as f(x) = |x|.

Front

How do you find the range of a piecewise function?

Back

To find the range, evaluate the output values of each piece of the function and determine the overall set of outputs.

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph.

Front

What is the notation for domain restrictions?

Back

Domain restrictions are often expressed using inequalities, such as -6 < x < 6.

Front

How do you evaluate f(x) for a piecewise function?

Back

To evaluate f(x), determine which piece of the function applies to the given x-value and use that expression.

Front

What is the significance of the vertex in an absolute value function?

Back

The vertex is the highest or lowest point of the graph, representing the minimum or maximum value of the function.

Front

How do you graph a piecewise function?

Back

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