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 its domain.

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

Back

This 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

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

Back

Substitute the specific point into the function and use the appropriate piece based on the value of x.

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 the point where the pieces of a piecewise function meet?

Back

The point where the pieces meet is called a breakpoint, and it is important for determining continuity and the overall behavior of the function.

Front

What is the difference between '≤' and '<' in piecewise functions?

Back

'≤' includes the endpoint in the interval, while '<' does not include the endpoint.

Front

How do 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 circles at endpoints based on the inequalities.

Front

What is the equation of the piece of a piecewise function that is defined for x > 3?

Back

The equation for x > 3 is determined by the expression that corresponds to that interval in the piecewise function.