Piecewise Practice

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 union of the domains of each piece, considering the conditions that define each piece.

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

How do you evaluate a piecewise function at a specific point?

Back

To evaluate a piecewise function at a specific point, determine which piece of the function applies to that point and then substitute the point into that piece.

Front

What is the value of f(2) for the function f(x) = { x if x < 4; -x+1 if x ≥ 4?

Back

f(2) = 2, since 2 is less than 4.

Front

What is the value of f(-7) for the function f(x) = { -x+1 if x < 4; x if x ≥ 4?

Back

f(-7) = -(-7) + 1 = 8, since -7 is less than 4.

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 the continuity of the function.

Front

How do you find the value of f(-1) for the function f(x) = { -x+1 if x < 4; x if x ≥ 4?

Back

f(-1) = -(-1) + 1 = 2, since -1 is less than 4.

Front

What is the value of f(6) for the function f(x) = { -x+1 if x < 4; x if x ≥ 4?

Back

f(6) = 6, since 6 is greater than or equal to 4.

Front

What is the result of 4f(-1) - f(6) - 2f(-6) for the function f(x) = { -x+1 if x < 4; x if x ≥ 4?

Back

4f(-1) - f(6) - 2f(-6) = 4(2) - 6 - 2(7) = 8 - 6 - 14 = -12.