Transformations of Parent Functions

Front

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

Back

A vertical translation occurs when a function is shifted up or down on the graph. For example, f(x) + k shifts the graph up by k units if k > 0 and down by k units if k < 0.

Front

How does the transformation f(x) = -f(x) affect the graph of a function?

Back

The transformation f(x) = -f(x) reflects the graph across the x-axis.

Front

What does the transformation f(x - h) represent?

Back

The transformation f(x - h) represents a horizontal shift of the graph to the right by h units if h > 0 and to the left by h units if h < 0.

Front

What is the effect of a horizontal stretch on the graph of a function?

Back

A horizontal stretch by a factor of k (where k > 1) compresses the graph horizontally, making it narrower, while a factor of k (where 0 < k < 1) stretches it, making it wider.

Front

Describe the transformation of the function y = f(-x).

Back

The transformation y = f(-x) reflects the graph across the y-axis.

Front

What does the transformation f(kx) do to the graph of a function?

Back

The transformation f(kx) compresses the graph horizontally by a factor of 1/k if k > 1, and stretches it horizontally by a factor of 1/k if 0 < k < 1.

Front

How does the transformation f(x) + k affect the graph?

Back

The transformation f(x) + k shifts the graph vertically. If k > 0, the graph shifts up by k units; if k < 0, it shifts down by |k| units.

Front

What is the result of applying the transformation f(-x) to a function?

Back

The transformation f(-x) reflects the graph of the function across the y-axis.

Front

Explain the transformation represented by y = -f(x) + k.

Back

The transformation y = -f(x) + k reflects the graph across the x-axis and then shifts it vertically by k units.

Front

What does the transformation f(x + 4) indicate?

Back

The transformation f(x + 4) indicates a horizontal shift of the graph to the left by 4 units.