Check In 3: 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

The domain of a piecewise function is the set of all possible input values (x) for which the function is defined, considering all pieces.

Front

What does it mean for a function to be increasing on an interval?

Back

A function is increasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) < f(x2).

Front

What does it mean for a function to be decreasing on an interval?

Back

A function is decreasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) > f(x2).

Front

What does it mean for a function to be constant on an interval?

Back

A function is constant on an interval if, for any two points x1 and x2 in that interval, f(x1) = f(x2).

Front

How do you find f(a) for a piecewise function?

Back

To find f(a), identify which piece of the function applies to the value a and then substitute a into that piece.

Front

What is the range of a piecewise function?

Back

The range of a piecewise function is the set of all possible output values (f(x)) that the function can produce.

Front

What is the significance of endpoints in piecewise functions?

Back

Endpoints determine whether the function includes or excludes certain values in its domain or range, affecting continuity.

Front

How do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece according to its defined interval, ensuring to use open or closed dots as needed.

Front

What is the difference between open and closed intervals?

Back

An open interval (a, b) does not include the endpoints a and b, while a closed interval [a, b] includes both endpoints.