Transformations Review

Front

What is a vertical stretch in transformations?

Back

A vertical stretch occurs when the graph of a function is stretched away from the x-axis by a factor greater than 1, making it taller.

Front

What does it mean to reflect a graph over the x-axis?

Back

Reflecting a graph over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

Describe the transformation of the function y = 2(x - 3)^2 + 1.

Back

This function represents a vertical stretch by a factor of 2, a shift right by 3, and a shift up by 1.

Front

What is a horizontal compression in transformations?

Back

A horizontal compression occurs when the graph of a function is compressed towards the y-axis by a factor greater than 1.

Front

How does a negative sign in front of a function affect its graph?

Back

A negative sign in front of a function reflects the graph over the x-axis.

Front

What does it mean to shift a graph left or right?

Back

Shifting a graph left means moving it in the negative x-direction, while shifting it right means moving it in the positive x-direction.

Front

What is the effect of a vertical shift on a graph?

Back

A vertical shift moves the graph up or down without changing its shape.

Front

Describe the transformation of the function y = -rac{1}{2}(x + 4)^3 - 3.

Back

This function represents a vertical compression by a factor of 2, a reflection over the x-axis, a shift left by 4, and a shift down by 3.

Front

What is the transformation of the function y = rac{1}{3}x^2 + 2?

Back

This function represents a vertical compression by a factor of 3 and a shift up by 2.

Front

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

Back

A vertical stretch by a factor of k means that the y-values of the function are multiplied by k, making the graph taller.