Transformations of Linear Functions

This lesson covers transformations of linear functions, including translations, dilations, and reflections. It explains how to perform vertical and horizontal translations, vertical and horizontal dilations, and reflections across the x-axis and y-axis. The lesson uses the parent linear function f(x) = x as a basis for demonstrating these transformations, providing examples and graphing techniques to illustrate each type of transformation.

What is the primary effect of a translation on a linear function?

• It moves the line up, down, left, or right.

• It flips the line across an axis.

• It changes the slope of the line.

• It stretches or compresses the line.

In a vertical translation, what happens when a constant is added to the parent function?

• The line moves down.

• The line moves left.

• The line moves right.

• The line moves up.

How does a horizontal translation affect the graph of a linear function?

• It flips the line across an axis.

• It changes the slope of the line.

• It moves the line up or down.

• It moves the line left or right.

What is the result of combining vertical and horizontal translations?

• The line only moves vertically.

• The line only moves horizontally.

• The line moves both vertically and horizontally.

• The line's slope changes.

What does a vertical dilation do to a linear function when the absolute value of the dilation factor is greater than one?

• It flips the line across the y-axis.

• It moves the line horizontally.

• It stretches the line away from the x-axis.

• It compresses the line toward the x-axis.

In horizontal dilation, what happens when the absolute value of the dilation factor is between 0 and 1?

• The line flips across the x-axis.

• The line moves vertically.

• The line stretches away from the y-axis.

• The line compresses toward the y-axis.

What is the effect of reflecting a linear function across the x-axis?

• The line moves up.

• The line flips horizontally.

• The line flips vertically.

• The line moves down.