Graph Transformations and Reflections

The video tutorial covers transformations of graphs, focusing on translation, dilation, and reflection. It explains how to shift graphs horizontally and vertically, stretch and compress them, and flip them across axes. The tutorial uses examples and visual aids to illustrate these concepts, encouraging the use of graphing tools like Desmos for better understanding.

What is the primary effect of a translation on a graph?

• It changes the graph's shape.

• It alters the graph's size.

• It shifts the graph's position.

• It reflects the graph.

If a graph of y = f(x) is transformed to y = f(x - a), what happens to the graph?

• It shifts a units down.

• It shifts a units to the left.

• It shifts a units to the right.

• It shifts a units up.

How does a vertical translation affect the graph of y = f(x)?

• It moves the graph up or down.

• It stretches the graph horizontally.

• It compresses the graph vertically.

• It moves the graph left or right.

What operation is used to perform a horizontal dilation on a graph?

• Addition

• Multiplication

• Subtraction

• Division

In a vertical dilation, what happens when y is divided by a constant?

• The graph shifts to the left.

• The graph shifts to the right.

• The graph becomes taller.

• The graph becomes wider.

What is the result of applying a horizontal reflection to a graph?

• The graph is stretched horizontally.

• The graph is flipped over the y-axis.

• The graph is flipped over the x-axis.

• The graph is compressed vertically.

How do you achieve a vertical reflection of a graph?

• By multiplying y by -1.

• By subtracting a constant from y.

• By dividing x by a constant.

• By adding a constant to x.

What transformation is applied to change an exponential growth graph to an exponential decay graph?

• Vertical reflection

• Horizontal reflection

• Horizontal translation

• Vertical translation

What does a vertical reflection do to an exponential graph?

• It stretches the graph vertically.

• It flips the graph over the x-axis.

• It flips the graph over the y-axis.

• It compresses the graph horizontally.

What is the result of applying both horizontal and vertical reflections to a graph?

• The graph is flipped in both directions.

• The graph is unchanged.

• The graph is stretched in both directions.

• The graph is rotated 90 degrees.