2.3 Review Transformations y = f(x) (Mixed)

Front

What is a vertical reflection in the context of function transformations?

Back

A vertical reflection occurs when the graph of a function is flipped over the x-axis, resulting in the transformation y = -f(x).

Front

What does a vertical stretch by a factor of 2 mean?

Back

A vertical stretch by a factor of 2 means that the y-values of the function are multiplied by 2, making the graph taller. This is represented by y = 2f(x).

Front

How does a horizontal shift to the right affect the graph of a function?

Back

A horizontal shift to the right by 'h' units is represented by y = f(x - h). It moves every point on the graph 'h' units to the right.

Front

What is the effect of a vertical shift up by 5 units on a function?

Back

A vertical shift up by 5 units is represented by y = f(x) + 5, moving every point on the graph up by 5 units.

Front

What does a horizontal compression by a factor of 1/2 mean?

Back

A horizontal compression by a factor of 1/2 means that the x-values of the function are halved, making the graph narrower. This is represented by y = f(2x).

Front

How do you represent a vertical reflection and a horizontal shift right 2 units?

Back

This transformation is represented by y = -f(x - 2), indicating a vertical reflection over the x-axis and a horizontal shift right.

Front

What is the transformation represented by y = f(-x)?

Back

The transformation y = f(-x) represents a horizontal reflection over the y-axis.

Front

If a function has a point (a, b), what are the new coordinates after a horizontal shift left 3 units?

Back

The new coordinates will be (a - 3, b).

Front

What does the transformation y = rac{2}{3}f(x) do to the graph?

Back

This transformation compresses the graph vertically by a factor of 2/3, making it shorter.

Front

How do you find the new coordinates after applying the transformation y = f(x + 4) - 2 to the point (1, 3)?

Back

The new coordinates will be (-3, 1) after shifting left 4 units and down 2 units.