General Transformations of Graphs

Front

What is a horizontal shift in the graph of a function?

Back

A horizontal shift occurs when the graph of a function is moved left or right along the x-axis. For example, the function y = f(x - 4) shifts the graph 4 units to the right.

Front

What does the transformation y = f(x + 3) represent?

Back

The transformation y = f(x + 3) represents a horizontal shift of the graph 3 units to the left.

Front

What is a vertical shift in the graph of a function?

Back

A vertical shift occurs when the graph of a function is moved up or down along the y-axis. For example, the function y = f(x) + 4 shifts the graph 4 units up.

Front

What does the transformation g(x) = f(x) - 6 represent?

Back

The transformation g(x) = f(x) - 6 represents a vertical shift of the graph 6 units down.

Front

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

Back

Multiplying a function by a negative number reflects the graph over the x-axis. For example, y = -f(x) reflects the graph of y = f(x) over the x-axis.

Front

What does the transformation y = f(2x) do to the graph?

Back

The transformation y = f(2x) compresses the graph horizontally by a factor of 2.

Front

What does the transformation y = f(0.5x) do to the graph?

Back

The transformation y = f(0.5x) stretches the graph horizontally by a factor of 2.

Front

What is the effect of a reflection over the y-axis?

Back

A reflection over the y-axis occurs when the function is transformed to y = f(-x), flipping the graph horizontally.

Front

What does the transformation y = f(x - 1) represent?

Back

The transformation y = f(x - 1) represents a horizontal shift of the graph 1 unit to the right.

Front

What does the transformation y = -2f(x - 1) + 2 represent?

Back

The transformation y = -2f(x - 1) + 2 represents a reflection over the x-axis, a vertical stretch by a factor of 2, a horizontal shift 1 unit to the right, and a vertical shift 2 units up.