Exploring Linear Transformations

This video tutorial covers linear function transformations, starting with the parent function y = x. It explains how to perform vertical and horizontal shifts, vertical stretches and shrinks, and reflections over the x-axis. The tutorial provides examples of each transformation, demonstrating how to adjust the function's equation accordingly. By the end, viewers will understand how to manipulate linear functions graphically and algebraically.

What is the parent function for a linear function?

• y = 2x

• y = x

• y = 1/x

• y = x^2

How do you move a linear function up by 2 units?

• Add 2 to the function

• Multiply the function by 2

• Subtract 2 from the function

• Divide the function by 2

What transformation is applied when you subtract a constant inside the parentheses?

• Move left

• Move down

• Move right

• Move up

What does a vertical stretch do to the slope of a line?

• Reflects it

• Flattens it

• Makes it steeper

• Makes it less steep

How do you reflect a linear function over the x-axis?

• Subtract 1

• Add 1

• Multiply by -1

• Multiply by 1

What is the result of a vertical shrink by a factor of 1/2 on the function y = 2x?

• y = 4x

• y = x

• y = 2x

• y = 1/2x

How do you move the function y = 2x to the left by 4 units?

• y = 2(x - 4)

• y = 2(x + 4)

• y = 2x + 4

• y = 2x - 4

What is the new function if you move y = 2x up by 5 units?

• y = 2(x + 5)

• y = 2x - 5

• y = 2(x - 5)

• y = 2x + 5

What is the result of reflecting y = 2x over the x-axis?

• y = -2x

• y = 2x

• y = 2(-x)

• y = -2(-x)

What is the simplified form of the function y = 2(x - 5) - 3?

• y = 2x + 8

• y = 2x - 8

• y = 2x - 13

• y = 2x + 13