Transformations: Stretch and Shrink

Transformations: Vertical and Horizontal Stretch and Shrink

Read each question carefully and apply your knowledge of vertical and horizontal stretches and shrinks to answer. Show all your work for short answer questions.

1. If the graph of y = f(x) is vertically stretched by a factor of 3, what is the equation of the new graph?

2. A horizontal shrink by a factor of 1/2 means that each x-coordinate is:

1. A vertical stretch makes the graph appear   (taller/shorter).

2. When a function f(x) is transformed to f(bx), if b > 1, the graph undergoes a horizontal   (stretch/shrink).

3. If a graph is horizontally stretched by a factor of 4, the new x-coordinates will be   the original x-coordinates.

1. Describe the transformation from f(x) to g(x) = 0.5f(x).

2. If the point (2, 4) is on the graph of y = f(x), what would be the corresponding point on the graph of y = f(2x)?

Consider the function f(x) = x². Plot the given points and then apply the specified transformation to find the new points. Sketch both the original and transformed graphs on the coordinate plane.

Original points for f(x) = x²: (-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4)

Transformation: Vertical stretch by a factor of 2. (i.e., g(x) = 2f(x))

1. A horizontal stretch by a factor of 3 means the graph becomes wider.

2. If 0 < a < 1, then y = af(x) represents a vertical shrink.