2.4 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?

Back

To evaluate a piecewise function, identify the interval in which the input value falls and use the corresponding expression to find the output.

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, meaning it can be drawn without lifting the pencil.

Front

What is 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

What is 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

How do you find the value of f(x) for a given x in a piecewise function?

Back

Substitute the given x value into the appropriate piece of the function based on its defined intervals.

Front

What is the significance of the graph of a piecewise function?

Back

The graph of a piecewise function visually represents how the function behaves over different intervals, showing changes in slope or value.

Front

What is an example of a piecewise function?

Back

An example is: f(x) = { x^2 for x < 0; 2x + 1 for x >= 0 }.

Front

What is a jump discontinuity?

Back

A jump discontinuity occurs when the left-hand limit and right-hand limit of a function at a certain point do not equal each other.

Front

How can you determine if a piecewise function is linear?

Back

A piecewise function is linear if each piece is a linear function (i.e., can be expressed in the form y = mx + b) over its interval.