Understanding Absolute Value Functions

The video tutorial explains the concepts of domain and range in functions, focusing on absolute value functions. It describes how the domain of absolute value functions is all real numbers and how the range is determined by the function's transformations. The tutorial also covers how to express domain and range using interval notation and other mathematical shorthand. Additionally, it discusses how transformations like shifts and reflections affect the range of absolute value functions.

What is the domain of a function?

• The set of all possible outputs of a function

• The set of X values that can be used in a function

• The set of Y values that result from a function

• The set of all possible inputs and outputs of a function

Which of the following is true for the domain of absolute value functions?

• It includes only negative numbers

• It includes only integers

• It includes only positive numbers

• It includes all real numbers

How can the domain of a function be expressed?

• Using only words

• Using interval notation, mathematical shorthand, or in words

• Using only interval notation

• Using only mathematical shorthand

What is the range of a function?

• The set of all possible inputs and outputs of a function

• The set of X values that can be used in a function

• The set of all possible inputs of a function

• The set of Y values that result from a function

For an absolute value function, what is the range?

• From negative infinity to zero

• From zero to infinity

• From zero to a finite number

• From negative infinity to positive infinity

How does adding or subtracting a number inside the absolute value affect the domain?

• It changes the domain to only positive numbers

• It changes the domain to only negative numbers

• It restricts the domain to integers

• It does not change the domain

What determines the range of a transformed absolute value function?

• The position of the vertex and the direction the graph opens

• The domain of the function

• The steepness of the graph

• The number of transformations applied