Exploring Linear Translations and Shifts

This video tutorial explains how to translate linear functions both horizontally and vertically. It provides examples of translating a function to the left and down, demonstrating the process of writing new function rules and graphing the results. The tutorial emphasizes understanding the notation and the effects of transformations on the graph.

What is the main focus of the video tutorial?

• Translating linear functions

• Solving quadratic equations

• Finding the roots of functions

• Graphing polynomial functions

When translating a function horizontally to the left by three units, what operation is performed on the x-variable?

• Subtract 3 from x

• Add 3 to x

• Divide x by 3

• Multiply x by 3

In the horizontal translation example, what is the new function G(x) if the original function is F(x) = x - 2?

• G(x) = x - 5

• G(x) = x + 1

• G(x) = x + 5

• G(x) = x - 1

What is the y-intercept of the new function after translating F(x) = x - 2 horizontally to the left by three units?

• 2

• 0

• 3

• 1

How does the graph of the new function compare to the original function after a horizontal translation?

• It shifts to the left

• It shifts down

• It shifts up

• It shifts to the right

What is the main difference in notation between horizontal and vertical translations?

• Horizontal translations add/subtract inside the parentheses, vertical translations outside

• Horizontal translations multiply inside the parentheses, vertical translations outside

• Horizontal translations divide inside the parentheses, vertical translations outside

• Horizontal translations add/subtract outside the parentheses, vertical translations inside

When translating a function vertically down by three units, what operation is performed on the function?

• Divide the function by 3

• Multiply the function by 3

• Subtract 3 from the function

• Add 3 to the function

In the vertical translation example, what is the new function G(x) if the original function is F(x) = x - 2?

• G(x) = x + 5

• G(x) = x + 1

• G(x) = x - 5

• G(x) = x - 1

What is the y-intercept of the new function after translating F(x) = x - 2 vertically down by three units?

• 1

• 0

• -5

• -2

How does the graph of the new function compare to the original function after a vertical translation?

• It shifts to the left

• It shifts to the right

• It shifts down

• It shifts up