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.

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.HSF.IF.A.2

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.

Tags

CCSS.HSF.IF.A.2

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.

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.HSF-IF.C.7B

Front

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

Back

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

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.HSF-IF.C.7B