Transformations of Linear Functions

The video tutorial covers the transformation of linear functions, focusing on translations and dilations. It explains how translations shift graphs without altering the slope, while dilations change the graph's size by a scale factor, affecting both the slope and y-intercept. The tutorial provides examples and visual explanations to illustrate these concepts.

What is a transformation in the context of linear functions?

• Adding a new point to the graph

• Mapping each point on the graph to a new location

• Removing a point from the graph

• A change in the color of the graph

Which of the following is a type of transformation?

• Translation

• Shearing

• Rotation

• Reflection

What remains unchanged during a translation of a linear function?

• The x-intercept

• The slope

• The entire graph

• The y-intercept

In a vertical translation, what happens when you add a value to the y-intercept?

• The graph moves right

• The graph moves up

• The graph moves left

• The graph moves down

How does a horizontal translation affect the x-values?

• It multiplies the x-values by a constant

• It subtracts a constant from the x-values

• It divides the x-values by a constant

• It adds a constant to the x-values

If a function f(x) = 5x + 3 is translated to g(x) = f(x) + 1, what is the translation?

• Up 2 units

• Down 2 units

• Up 1 unit

• Down 1 unit

What is the effect of a negative value inside the parentheses in a translation?

• Moves the graph down

• Moves the graph up

• Moves the graph right

• Moves the graph left

What is a dilation in the context of linear functions?

• A change in the slope only

• A change in the y-intercept only

• A change in both slope and y-intercept

• A change in the x-intercept only

What happens to the graph during a vertical stretch?

• It becomes flatter

• It moves to the right

• It becomes steeper

• It moves to the left

In a vertical compression, what is the range of the K value?

• Less than 0

• Greater than 1

• Equal to 1

• Between 0 and 1