Exploring Linear Transformations

This video tutorial covers linear transformations, focusing on parent linear functions and their transformations. It explains vertical and horizontal shifts, vertical stretch and compression, and reflections. The tutorial provides detailed examples and descriptions of how these transformations affect the graph of a linear function, emphasizing the changes in slope, y-intercept, and x-intercept.

What is the parent linear function?

• y = x

• y = 2x

• y = x + 1

• y = x - 1

In the parent linear function y = x, what is the slope?

• 2

• Undefined

• 1

• 0

What does a vertical shift do to a graph?

• Reflects it over the x-axis

• Moves it up or down

• Changes its slope

• Moves it left or right

If f(x) = x, what is g(x) = f(x) + 1?

• A vertical shift up by 1

• A vertical shift down by 1

• A horizontal shift right by 1

• A horizontal shift left by 1

What does a horizontal shift do to a graph?

• Reflects it over the y-axis

• Moves it left or right

• Moves it up or down

• Changes its slope

If f(x) = x, what is g(x) = f(x - 2)?

• A horizontal shift right by 2

• A vertical shift up by 2

• A vertical shift down by 2

• A horizontal shift left by 2

What does a vertical stretch do to a graph?

• Reflects it over the x-axis

• Moves it left or right

• Makes it flatter

• Makes it steeper

If f(x) = x, what is g(x) = 2f(x)?

• A reflection over the x-axis

• A vertical shift up by 2

• A vertical stretch by a factor of 2

• A horizontal shift right by 2

What does a reflection do to a graph?

• Reflects it over the y-axis

• Reflects it over the x-axis

• Changes its slope

• Moves it up or down

If f(x) = x, what is g(x) = -f(x)?

• A horizontal shift left by 1

• A reflection over the x-axis

• A vertical stretch by a factor of -1

• A vertical shift down by 1