Transformations: Reflections, Stretches, Compressions

Front

What is a reflection in transformations?

Back

A reflection is a transformation that flips a function over a specified axis, such as the x-axis or y-axis.

Front

What does a vertical stretch do to a function?

Back

A vertical stretch increases the distance between points on the graph and the x-axis, making the graph taller.

Front

What does a vertical compression do to a function?

Back

A vertical compression decreases the distance between points on the graph and the x-axis, making the graph shorter.

Front

What is the effect of the transformation y = -f(x)?

Back

This transformation reflects the graph of f(x) over the x-axis.

Front

What is the effect of the transformation y = f(-x)?

Back

This transformation reflects the graph of f(x) over the y-axis.

Front

What does the transformation y = kf(x) do when k > 1?

Back

When k > 1, the transformation results in a vertical stretch of the graph.

Front

What does the transformation y = kf(x) do when 0 < k < 1?

Back

When 0 < k < 1, the transformation results in a vertical compression of the graph.

Front

What is the effect of the transformation y = f(x) + c?

Back

This transformation shifts the graph of f(x) vertically by c units. If c is positive, it shifts up; if negative, it shifts down.

Front

What is the effect of the transformation y = f(x + c)?

Back

This transformation shifts the graph of f(x) horizontally by c units. If c is positive, it shifts left; if negative, it shifts right.

Front

What does the transformation y = af(bx) do when a > 1 and b > 1?

Back

This transformation results in a vertical stretch (a > 1) and a horizontal compression (b > 1) of the graph.