Find the critical values of an absolute value function

The video tutorial discusses the concept of absolute value and its representation as a function. It explores graph transformations, including reflections and shifts, and how these affect the graph's appearance. The tutorial also delves into the concept of derivatives, explaining why certain graphs do not have horizontal tangents and identifying critical values where the derivative does not exist.

What is the purpose of rewriting a function using transformations?

• To understand the graph's shape

• To find the exact derivative

• To solve algebraic equations

• To simplify the function

Which transformation occurs when a negative sign is multiplied outside a function?

• Shifting to the right

• Shifting upwards

• Reflecting the Y-axis

• Reflecting the X-axis

What happens to a graph when you subtract a number inside the function?

• It reflects over the Y-axis

• It shifts to the right

• It shifts to the left

• It reflects over the X-axis

What are we looking for when the derivative is set to zero?

• Critical points

• Horizontal tangents

• Vertical tangents

• Inflection points

Why does the graph discussed not have a horizontal tangent?

• The graph is a straight line

• The graph is a circle

• The derivative does not exist

• The derivative is always positive