12.5.24 PAP Graphing 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 evaluate a piecewise function?

Back

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

Front

What does the notation f(x) = { x if x < 4; -x + 1 if x ≥ 4 mean?

Back

This notation means that for values of x less than 4, f(x) equals x, and for values of x greater than or equal to 4, f(x) equals -x + 1.

Front

What is the importance of the domain in piecewise functions?

Back

The domain specifies the input values for which the function is defined, and it helps determine which piece of the function to use for evaluation.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function on its respective interval, ensuring to use open or closed dots based on whether the endpoints are included.

Front

What is the difference between a closed dot and an open dot on a graph?

Back

A closed dot indicates that the endpoint is included in the function (≤ or ≥), while an open dot indicates that the endpoint is not included (< or >).

Front

What is the output of f(x) = 2x + 1 when x = 4?

Back

The output is f(4) = 2(4) + 1 = 9.

Front

How do you match a graph to its piecewise function?

Back

To match a graph to its piecewise function, analyze the slopes and intercepts of the lines in the graph and compare them to the expressions in the piecewise function.

Front

What is the significance of the breakpoints in piecewise functions?

Back

Breakpoints are the values where the function changes from one expression to another, and they are crucial for determining the behavior of the function.

Front

What does it mean if a piecewise function is continuous at a breakpoint?

Back

A piecewise function is continuous at a breakpoint if the limit from the left equals the limit from the right and both equal the function value at that point.