Function Transformations

Front

What is a function transformation?

Back

A function transformation refers to the changes made to the graph of a function, which can include shifts, stretches, compressions, and reflections.

Front

What does a vertical translation of a function involve?

Back

A vertical translation involves shifting the graph of a function up or down along the y-axis.

Front

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

Back

The transformation f(x) + k shifts the graph of f(x) vertically by k units; if k is positive, it shifts up, and if k is negative, it shifts down.

Front

What does the transformation f(x + h) do to the graph of f(x)?

Back

The transformation f(x + h) shifts the graph of f(x) horizontally by h units; if h is positive, it shifts left, and if h is negative, it shifts right.

Front

What is the effect of multiplying a function by a negative number?

Back

Multiplying a function by a negative number reflects the graph across the x-axis.

Front

What is a horizontal compression?

Back

A horizontal compression occurs when the input of a function is multiplied by a factor greater than 1, which makes the graph narrower.

Front

What is a horizontal stretch?

Back

A horizontal stretch occurs when the input of a function is multiplied by a factor between 0 and 1, which makes the graph wider.

Front

What does the transformation h(x) = f(x) - 2 represent?

Back

The transformation h(x) = f(x) - 2 represents a vertical translation of the graph of f(x) down by 2 units.

Front

What type of transformation is represented by g(x) = f(x + 3) - 2?

Back

The transformation g(x) = f(x + 3) - 2 represents a horizontal shift left by 3 units and a vertical shift down by 2 units.

Front

What is the parent function of a square root function?

Back

The parent function of a square root function is f(x) = √x.