Transformations of Functions

Front

What is a horizontal stretch of a function?

Back

A horizontal stretch occurs when the function is transformed by a factor greater than 1, making the graph wider. For example, y = f(1/5x) stretches the graph horizontally by a factor of 5.

Front

What is a vertical stretch of a function?

Back

A vertical stretch occurs when the function is transformed by a factor greater than 1, making the graph taller. For example, y = 5f(x) stretches the graph vertically by a factor of 5.

Front

What does the transformation g(x) = (x - 3)² represent?

Back

This transformation represents a horizontal shift of the graph of f(x) = x² to the right by 3 units.

Front

What does the transformation g(x) = x² + 3 represent?

Back

This transformation represents a vertical shift of the graph of f(x) = x² upwards by 3 units.

Front

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

Back

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

Front

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

Back

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

Front

What is a vertical shrink of a function?

Back

A vertical shrink occurs when the function is transformed by a factor between 0 and 1, making the graph shorter. For example, y = (1/5)f(x) shrinks the graph vertically by a factor of 1/5.

Front

What does the transformation g(x) = (x + 5)² represent?

Back

This transformation represents a horizontal shift of the graph of f(x) = x² to the left by 5 units.

Front

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

Back

This transformation compresses the graph of f(x) horizontally by a factor of 1/2.

Front

What does the transformation g(x) = x³ - 1 do?

Back

This transformation represents a vertical shift of the graph of f(x) = x³ downwards by 1 unit.