Understanding Transformations in Functions

The video tutorial explains how to find the domain and range of the function y = |7 - x|. It covers the parent function's properties, the impact of transformations, and how these transformations affect the graph's domain and range. The tutorial emphasizes understanding transformations like reflection and shifting, and how they apply to various functions.

What is the first step in evaluating a function?

• Find the range

• Evaluate the domain

• Identify the function type

• Graph the function

What shape does the graph of an absolute value function typically have?

• L-shaped

• S-shaped

• V-shaped

• U-shaped

What is the domain of the absolute value function y = |7 - x|?

• Only negative numbers

• Only positive numbers

• Numbers greater than 7

• All real numbers

What is the range of the absolute value function y = |7 - x|?

• All real numbers

• From -7 to 7

• From -infinity to 0

• From 0 to infinity

What is the purpose of understanding transformations in functions?

• To understand graph shifts and reflections

• To change the function type

• To identify the domain

• To calculate the range

Why is it important to rearrange functions?

• To find the domain

• To change the function type

• To identify transformations easily

• To simplify calculations

What does the 'a' in the transformation formula a(bx - c) + d represent?

• Vertical shift

• Reflection

• Vertical stretch or compression

• Horizontal shift

What happens when you factor out a negative in a function?

• It simplifies the function

• It helps identify transformations

• It changes the range

• It changes the domain

What is the effect of a negative 'b' in the transformation formula?

• Horizontal stretch

• Reflection about the x-axis

• Reflection about the y-axis

• Vertical shift

How do horizontal transformations affect the range of a function?

• They invert the range

• They do not affect the range

• They restrict the range

• They expand the range