Function Transformations

Front

What is a function transformation?

Back

A function transformation refers to the process of changing the position, size, or shape of the graph of a function.

Front

What does a vertical stretch of a function look like?

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 the effect of subtracting a constant from a function?

Back

Subtracting a constant from a function shifts the graph downward by that constant value.

Front

How does adding a constant inside the function affect the graph?

Back

Adding a constant inside the function shifts the graph horizontally; specifically, it translates the graph to the left if the constant is positive and to the right if negative.

Front

What is the transformation represented by g(x) = 2f(x)?

Back

The transformation g(x) = 2f(x) represents a vertical stretch of the function f(x) by a factor of 2.

Front

What does the transformation g(x) = f(x) - 9 indicate?

Back

The transformation g(x) = f(x) - 9 indicates that the graph of f(x) is shifted down 9 units.

Front

What is a horizontal translation in function transformations?

Back

A horizontal translation moves the graph of a function left or right along the x-axis.

Front

What transformation occurs when g(x) = (x + 4)²?

Back

The transformation g(x) = (x + 4)² represents a horizontal translation of the graph of f(x) = x², moving it 4 units to the left.

Front

What is the effect of multiplying a function by a factor less than 1?

Back

Multiplying a function by a factor less than 1 results in a vertical compression of the graph.

Front

What is the general form of a vertical stretch transformation?

Back

The general form of a vertical stretch transformation is g(x) = kf(x), where k > 1.