1.7 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 intervals of the input variable.

Front

How do you determine the output of a piecewise function?

Back

To determine the output, identify which interval the input value falls into and use the corresponding expression to calculate the output.

Front

What does the notation f(x) mean in a piecewise function?

Back

f(x) represents the output of the function for a given input x.

Front

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

Back

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

Front

What is the significance of the 'pieces' in a piecewise function?

Back

The 'pieces' represent different rules or formulas that apply to different sections of the domain.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece according to its defined interval and ensure to use open or closed dots based on whether the endpoints are included.

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 (y) that the function can produce.

Front

How do you evaluate a piecewise function at a specific point?

Back

To evaluate, find the interval that contains the specific point and apply the corresponding formula.

Front

What does it mean if a piecewise function has a discontinuity?

Back

A discontinuity means there is a jump or break in the graph of the function, indicating that the function is not continuous at that point.