Understanding Absolute Value Functions

Mr. Appel explains how to convert absolute value functions into piecewise functions. He begins by defining absolute value and demonstrates the conversion process with examples, including a function with two absolute values. The video concludes with graphing the piecewise function, illustrating the changes visually.

What is the first step in converting an absolute value function to a piecewise function?

• Graph the function

• Identify the non-negative regions

• Simplify the expression

• Solve for x

How is the absolute value of a positive number defined?

• It is the reciprocal of the number

• It is zero

• It is the negative of the number

• It is the number itself

What happens to the absolute value of a negative number?

• It becomes undefined

• It becomes positive

• It remains negative

• It becomes zero

In algebraic terms, what do you get if the expression inside the absolute value is non-negative?

• The expression itself

• A constant value

• The opposite of the expression

• Zero

What inequality is used to determine when an expression inside an absolute value is non-negative?

• x >= 0

• x <= 0

• x < 0

• x > 0

When converting to a piecewise function, what is the expression when x is less than 5?

• -(x + 5)

• x + 5

• -(x - 5)

• x - 5

What is the first step in dealing with functions that have two absolute values?

• Simplify the expression

• Determine when each expression is non-negative

• Graph the function

• Solve for x

What are the three regions identified for expressions with two absolute values?

• x < -3, -3 <= x <= 5, x > 5

• x < 0, 0 <= x <= 5, x > 5

• x < -5, -5 <= x <= 3, x > 3

• x < -2, -2 <= x <= 4, x > 4

What is the expression when both parts are negative?

• 2x - 2

• -2x + 2

• x + 5

• x - 5

What is the value of the function when one part is positive and the other is negative?

• x - 5

• x + 5

• 2x - 2

• A constant value