Absolute Value and Piecewise Functions

The video tutorial explains absolute values and how to express absolute value functions as piece-wise defined functions. It covers the basic properties of absolute values, such as the absolute value of a positive number being the number itself and the absolute value of a negative number being its opposite. The tutorial provides examples of converting absolute value expressions into piece-wise functions and solving inequalities, emphasizing the importance of understanding these concepts for evaluating limits of absolute value functions.

What is the absolute value of a positive number?

• Zero

• Double the number

• The negative of the number

• The number itself

What is the absolute value of a negative number?

• The positive of the number

• Zero

• The number itself

• The negative of the number

How can you express the opposite of a number algebraically?

• Square the number

• Divide by 2

• Multiply by -1

• Add 1 to the number

What is the piece-wise definition of an absolute value function when the input is positive?

• The output is the input itself

• The output is zero

• The output is double the input

• The output is the negative of the input

What happens to the absolute value function when the input is zero?

• The output is zero

• The output is one

• The output is negative

• The output is undefined

What is the purpose of writing absolute value functions as piece-wise functions?

• To increase their domain

• To decrease their range

• To make them more complex

• To evaluate limits more easily

What is the general rule for the absolute value of a variable 'triangle'?

• Zero if triangle is positive

• Triangle if triangle is positive

• Negative triangle if triangle is positive

• Triangle if triangle is negative

What is the result of multiplying a number by negative one?

• Double the number

• The number itself

• The negative of the number

• Zero

What is the absolute value of zero?

• Undefined

• Negative one

• One

• Zero

In a piece-wise function, what is the output when the input is negative?

• Zero

• The input itself

• The square of the input

• The negative of the input