Transformations of Linear Functions in Algebra 1

This video tutorial covers transformations of linear functions, including translations, vertical and horizontal shifts, stretching, compressing, and reflections. It explains how these transformations affect the position and shape of graphs on the coordinate plane. The tutorial also demonstrates how to combine multiple transformations and provides examples to illustrate each concept.

What is the primary focus of this lesson?

• Exponential functions

• Quadratic functions

• Polynomial functions

• Transformations of linear functions

What happens to a graph when a positive constant is added to f(x)?

• It moves down

• It moves up

• It moves right

• It moves left

If f(x) = x and we change it to f(x) = x - 3, what happens to the graph?

• It moves up by 3 units

• It moves down by 3 units

• It moves left by 3 units

• It moves right by 3 units

What does it mean when a graph is horizontally compressed?

• It moves down

• It moves up

• It gets closer to the x-axis

• It gets closer to the y-axis

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

• The graph gets closer to the x-axis

• The graph gets closer to the y-axis

• The graph moves right

• The graph moves left

What happens to a graph when it is reflected over the x-axis?

• It flips horizontally

• It flips vertically

• It moves down

• It moves up

If a graph is reflected over the y-axis, what happens?

• It moves up

• It moves down

• It flips horizontally

• It flips vertically

In the equation f(x) = -x + 2, what transformation occurs?

• Reflection over the y-axis

• Vertical stretch

• Horizontal compression

• Reflection over the x-axis

What is the combined effect of a vertical stretch and a reflection over the x-axis?

• The graph moves up and flips horizontally

• The graph gets less steep and flips vertically

• The graph moves down and flips horizontally

• The graph gets steeper and flips vertically

If f(x) = x is transformed to f(x) = -3(x + 2), what are the transformations?

• Reflection over the y-axis, vertical compression by 3, move right by 2

• Reflection over the x-axis, vertical stretch by 3, move left by 2

• Reflection over the y-axis, vertical stretch by 3, move left by 2

• Reflection over the x-axis, vertical compression by 3, move right by 2