Transformations of Linear Functions

This video tutorial covers transformations of linear functions, focusing on horizontal and vertical translations. It explains how translations shift the graph without changing its shape or size. Vertical translations involve adding a constant K to the output, moving the graph up or down. Horizontal translations involve subtracting a constant H from the input, moving the graph left or right. Examples are provided to illustrate these concepts.

What is a transformation in the context of linear functions?

• A change in the shape or size of the graph.

• A shift of the graph vertically or horizontally.

• A reflection of the graph over the x-axis.

• A rotation of the graph around the origin.

In a vertical translation, what happens when K is positive?

• The graph moves down.

• The graph shifts to the left.

• The graph shifts to the right.

• The graph moves up.

What is the general form of a vertically translated function?

• G(x) = f(x) + H

• G(x) = f(x) - H

• G(x) = f(x) - K

• G(x) = f(x) + K

How does a negative K value affect a vertical translation?

• The graph moves left.

• The graph moves down.

• The graph moves right.

• The graph moves up.

What is the effect of adding a positive K to f(x) in a vertical translation?

• The graph moves up.

• The graph shifts right.

• The graph shifts left.

• The graph moves down.

If f(x) = 2x + 3 is translated four units up, what is the new function G(x)?

• G(x) = 2x - 1

• G(x) = 2x + 1

• G(x) = 2x + 7

• G(x) = 2x + 3

What is the effect of a horizontal translation with a positive H?

• The graph moves up.

• The graph moves right.

• The graph moves down.

• The graph moves left.

What is the rule for a horizontal translation?

• Subtract H from the output value.

• Subtract H from the input value.

• Add H to the input value.

• Add H to the output value.

If H is negative in a horizontal translation, what happens to the graph?

• It moves right.

• It moves left.

• It moves down.

• It moves up.

What is the result of a horizontal translation with H = -2?

• The graph moves 2 units down.

• The graph moves 2 units left.

• The graph moves 2 units right.

• The graph moves 2 units up.