Transformations in Function Notation

Front

What is a vertical translation in function notation?

Back

A vertical translation occurs when a constant is added to or subtracted from a function, shifting the graph up or down. For example, g(x) = f(x) + k translates the graph of f vertically by k units.

Front

How does a reflection over the x-axis affect the graph of a function?

Back

A reflection over the x-axis inverts the y-values of the function. This is represented in function notation as g(x) = -f(x), where the graph of f is flipped over the x-axis.

Front

What does a vertical stretch by a factor of k mean in function notation?

Back

A vertical stretch by a factor of k means that the y-values of the function are multiplied by k, making the graph taller. This is represented as g(x) = k*f(x), where k > 1.

Front

What is a horizontal translation in function notation?

Back

A horizontal translation occurs when a constant is added to or subtracted from the input of a function, shifting the graph left or right. For example, g(x) = f(x - h) translates the graph of f horizontally by h units.

Front

Describe the transformation represented by g(x) = f(x) + 3.5.

Back

This represents a vertical translation of the graph of f upwards by 3.5 units.

Front

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

Back

This represents a reflection of the graph of f over the x-axis.

Front

Describe the transformation represented by g(x) = f(x) - 2.8.

Back

This represents a vertical translation of the graph of f downwards by 2.8 units.

Front

What does g(x) = (7/3)f(x + 2) represent in terms of transformations?

Back

This represents a horizontal translation of the graph of f left by 2 units and a vertical stretch by a factor of 7/3.

Front

Describe the transformation represented by g(x) = f(x + 8).

Back

This represents a horizontal translation of the graph of f left by 8 units.

Front

What is the effect of adding a positive constant to a function in function notation?

Back

Adding a positive constant to a function results in a vertical translation of the graph upwards.