Piecewise Practice 2

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 determine the range of a piecewise function?

Back

To determine the range, evaluate the output values of each piece of the function over its defined domain and combine the results.

Front

What does the notation (-∞, 4] represent?

Back

The notation (-∞, 4] represents all real numbers less than or equal to 4.

Front

What are domain restrictions in a piecewise function?

Back

Domain restrictions specify the values of x for which a particular piece of the function is valid.

Front

How do you find the value of f(x) at a specific point in a piecewise function?

Back

To find f(x) at a specific point, identify which piece of the function applies to that x value and evaluate it using the corresponding formula.

Front

What does the notation 1 ≤ x < 3 mean?

Back

The notation 1 ≤ x < 3 means x is greater than or equal to 1 and less than 3.

Front

What is the significance of the endpoints in a piecewise function?

Back

Endpoints indicate whether the value at that point is included in the domain (closed interval) or excluded (open interval).

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 as appropriate.

Front

What is the difference between open and closed intervals?

Back

An open interval does not include its endpoints, while a closed interval includes its endpoints.

Front

What is the value of f(0) if f(x) = 4 for -2 < x ≤ 1?

Back

f(0) = 4, since 0 falls within the interval -2 < x ≤ 1.