Writing Transformations of Functions

Front

What is a vertical shift in function transformations?

Back

A vertical shift moves the graph of a function up or down without changing its shape. For example, if f(x) is shifted up by 3, the new function is f(x) + 3.

Front

What does a horizontal shift do to a function?

Back

A horizontal shift moves the graph of a function left or right. For example, f(x + 2) shifts the graph 2 units to the left.

Front

Define a vertical stretch in function transformations.

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller. For example, if f(x) is stretched by a factor of 2, the new function is 2f(x).

Front

What is a vertical shrink in function transformations?

Back

A vertical shrink occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph shorter. For example, if f(x) is shrunk by a factor of 0.5, the new function is 0.5f(x).

Front

Explain what a reflection across the x-axis means.

Back

A reflection across the x-axis flips the graph of a function over the x-axis. For example, if f(x) is reflected, the new function is -f(x).

Front

What does a reflection across the y-axis entail?

Back

A reflection across the y-axis flips the graph of a function over the y-axis. For example, if f(x) is reflected, the new function is f(-x).

Front

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

Back

This represents a horizontal shift of the function f(x) to the right by 3 units.

Front

What transformation does g(x) = f(x) + 4 represent?

Back

This represents a vertical shift of the function f(x) upward by 4 units.

Front

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

Back

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

Front

What does the transformation g(x) = f(x + 5) do to the graph?

Back

This transformation shifts the graph of f(x) to the left by 5 units.