Effects of Graph Stretches and Transformations

This tutorial covers the concept of graph transformations, focusing on stretches. It explains vertical and horizontal stretching, demonstrating how multiplying a function by a constant affects its graph. The tutorial provides examples of stretching parallel to the y-axis and x-axis, including cases where the scale factor is a fraction. Key points and invariant points are discussed to illustrate the effects of these transformations.

What is the main focus of this tutorial?

• Graph reflections

• Graph stretches

• Graph rotations

• Graph translations

What happens to a graph when it is stretched vertically by a factor of 2?

• It halves in height

• It doubles in height

• It becomes narrower

• It becomes wider

What is an invariant point in the context of vertical stretches?

• A point that doubles in height

• A point that remains unchanged

• A point that moves down

• A point that moves up

If a graph is stretched vertically by a factor of 0.5, what happens to its height?

• It halves

• It remains the same

• It triples

• It doubles

What is the effect of multiplying a function by a number less than one?

• The graph stretches vertically

• The graph compresses vertically

• The graph stretches horizontally

• The graph compresses horizontally

What is the main difference between vertical and horizontal stretches?

• Horizontal stretches affect height

• Vertical stretches affect width

• Horizontal stretches affect color

• Vertical stretches affect height

How is a horizontal stretch different from a vertical stretch?

• It does not affect the graph

• It affects both axes

• It affects the y-axis

• It affects the x-axis

What happens to a point 2 units to the left of the y-axis during a horizontal stretch by a factor of 0.5?

• It remains at 2 units left

• It moves to 3 units left

• It moves to 4 units left

• It moves to 1 unit left

What is the result of replacing x with 2x in a function?

• A horizontal stretch by a factor of 2

• A vertical stretch by a factor of 2

• A horizontal stretch by a factor of 0.5

• A vertical stretch by a factor of 0.5

What is the effect of replacing x with 0.5x in a function?

• A vertical stretch by a factor of 2

• A horizontal stretch by a factor of 2

• A horizontal stretch by a factor of 0.5

• A vertical stretch by a factor of 0.5