Transformations in Function Notation

Front

What is a horizontal translation in function notation?

Back

A horizontal translation involves shifting the graph of a function left or right along the x-axis. For example, g(x) = f(x + c) translates the graph left by c units, while g(x) = f(x - c) translates it right by c units.

Front

How does a vertical translation affect the graph of a function?

Back

A vertical translation shifts the graph of a function up or down along the y-axis. For instance, g(x) = f(x) + k moves the graph up by k units, while g(x) = f(x) - k moves it down by k units.

Front

What does a reflection over the y-axis mean in function notation?

Back

A reflection over the y-axis occurs when the function is transformed to g(x) = f(-x). This flips the graph horizontally across the y-axis.

Front

What is a vertical shrink in function notation?

Back

A vertical shrink occurs when the output of the function is multiplied by a factor between 0 and 1. For example, g(x) = k*f(x) where 0 < k < 1 results in a vertical shrink by a factor of k.

Front

Describe the transformation represented by g(x) = f(x + 5).

Back

This represents a horizontal translation of the graph of f left by 5 units.

Front

Describe the transformation represented by g(x) = f(x - 3).

Back

This represents a horizontal translation of the graph of f right by 3 units.

Front

What does the transformation g(x) = -f(x) indicate?

Back

This indicates a reflection of the graph of f over the x-axis.

Front

How does the transformation g(x) = f(x) + 4 affect the graph?

Back

This transformation shifts the graph of f up by 4 units.

Front

What is the effect of the transformation g(x) = 2f(x)?

Back

This transformation results in a vertical stretch of the graph of f by a factor of 2.

Front

What does the transformation g(x) = f(-x) do to the graph?

Back

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