Retake/Practice Piece-wise 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 does the notation f(x) = { x if x < 4; -x + 1 if x ≥ 4 mean?

Back

This notation 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

What is the domain of a piecewise function?

Back

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

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) values) that the function can produce.

Front

How do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function according to its defined interval, ensuring to use open or closed circles to indicate whether endpoints are included.

Front

What does the statement 6 < x < 10 mean?

Back

It means any number between 6 and 10, but not including 6 and 10.

Front

What is the value of f(1) if f(x) = { 3 if x < 2; 1 if x = 2; 0 if x > 2?

Back

f(1) = 3, since 1 is less than 2.

Front

What is the value of g(7) if g(x) = { -2x + 1 if x < 5; 2x - 1 if x ≥ 5?

Back

g(7) = 2(7) - 1 = 14 - 1 = 13.

Front

How do you determine continuity in piecewise functions?

Back

A piecewise function is continuous if there are no breaks, jumps, or holes in the graph, particularly at the points where the pieces meet.