Transformations of Linear and Absolute Value Functions

This video tutorial covers lesson 1.2 on transformations of linear and absolute value functions. It begins with an introduction to transformations, focusing on horizontal and vertical stretches and shrinks. The tutorial explains how these transformations affect the graph of a function, using both algebraic and graphical representations. The video also provides examples of how to apply these transformations to specific functions, highlighting the importance of understanding the reciprocal relationship in horizontal transformations and the direct relationship in vertical transformations.

What transformations were covered in the previous lesson?

• Horizontal and vertical shifting, and reflecting over the x-axis and y-axis

• Horizontal and vertical stretching, and reflecting over the x-axis and y-axis

• Horizontal and vertical shrinking, and reflecting over the x-axis and y-axis

• Horizontal and vertical rotating, and reflecting over the x-axis and y-axis

What happens to a line when you perform a horizontal stretch?

• The line becomes more gradual

• The line becomes steeper

• The line shifts vertically

• The line reflects over the y-axis

When 'a' is greater than 1, what happens to the line?

• The line becomes more gradual

• The line becomes steeper

• The line shifts horizontally

• The line reflects over the x-axis

What is the effect on the line when 'a' is between 0 and 1?

• The line becomes more gradual

• The line becomes steeper

• The line shifts vertically

• The line reflects over the y-axis

What is the difference between horizontal and vertical stretches in terms of the 'a' value?

• Both use 'a' directly

• Both use the reciprocal of 'a'

• Horizontal stretches use 'a' directly, vertical stretches use the reciprocal of 'a'

• Horizontal stretches use the reciprocal of 'a', vertical stretches use 'a' directly

In a vertical stretch, what happens to the line when 'a' is greater than 1?

• The line reflects over the x-axis

• The line becomes steeper

• The line becomes more gradual

• The line shifts horizontally

How do you represent a horizontal shrink algebraically?

• Replace y with y/a in the function

• Replace y with ay in the function

• Replace x with x/a in the function

• Replace x with ax in the function

What is the algebraic representation of a vertical stretch by a factor of 2?

• 2 * f(x)

• f(x) + 2

• f(2x)

• f(x/2)

What is the effect of a vertical stretch on the graph of a function?

• The graph is pulled away from the x-axis

• The graph is pulled towards the x-axis

• The graph is pulled away from the y-axis

• The graph is pulled towards the y-axis

In the example given, what is the final form of the function after a horizontal shrink by a factor of 1/3?

• Absolute value of 3x - 1 - 5

• Absolute value of x/3 - 3 - 5

• Absolute value of x - 3 - 5

• Absolute value of 3x - 3 - 5