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 determine the domain of a piecewise function?

Back

To determine the domain, identify the intervals for which each piece of the function is defined and combine them.

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, which may depend on which piece of the function is applicable.

Front

What is the significance of the domain restrictions in piecewise functions?

Back

Domain restrictions indicate the values of x for which the function is defined, ensuring that the function behaves correctly.

Front

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

Back

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

Front

What is the output of f(2) if f(x) = { 3 for x < 2, 4 for x = 2, 5 for x > 2 }?

Back

4

Front

What is the output of g(7) if g(x) = { -x - 10 for x < 0, 2x + 3 for x >= 0 }?

Back

17

Front

What is the range of a piecewise function?

Back

The range is the set of all possible output values of the function, determined by evaluating each piece over its domain.

Front

How can you graph a piecewise function?

Back

To graph, plot each piece of the function on its respective interval, using open or closed dots to indicate inclusivity.

Front

What is the difference between a closed interval and an open interval?

Back

A closed interval includes its endpoints (e.g., [a, b]), while an open interval does not (e.g., (a, b)).