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 shift of a function mean?

Back

A vertical shift moves the graph of the function up or down without changing its shape.

Front

What is the effect of adding a constant to a function, f(x) + k?

Back

Adding a constant k to a function shifts the graph vertically. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

What does f(x - h) represent?

Back

The expression f(x - h) represents a horizontal shift of the graph to the right by h units.

Front

What does f(x + h) represent?

Back

The expression f(x + h) represents a horizontal shift of the graph to the left by h units.

Front

What is a vertical stretch of a function?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

Front

What is a vertical compression of a function?

Back

A vertical compression occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph shorter.

Front

What does a negative sign in front of a function indicate?

Back

A negative sign in front of a function reflects the graph across the x-axis.

Front

What is the transformation of g(x) = f(x) + 5?

Back

The transformation g(x) = f(x) + 5 shifts the graph of f(x) up by 5 units.

Front

What is the transformation of g(x) = f(x - 3)?

Back

The transformation g(x) = f(x - 3) shifts the graph of f(x) to the right by 3 units.