Function Transformations

Front

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

Back

The graph of f(x) is translated up 2 units.

Front

What does the transformation g(x) = f(x + 3) do to the graph of f(x)?

Back

The graph of f(x) is translated left 3 units.

Front

If g(x) = f(x) - 5, how does this transformation affect the graph of f(x)?

Back

The graph of f(x) is translated down 5 units.

Front

What is the transformation rule for g(x) if f(x) is translated 2 units up and vertically shrunk with a scale factor of 0.5?

Back

g(x) = 0.5f(x) + 2.

Front

What does the transformation g(x) = f(x - 7) indicate about the graph of f(x)?

Back

The graph of f(x) is translated right 7 units.

Front

What is a vertical shift in function transformations?

Back

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

Front

What is a horizontal shift in function transformations?

Back

A horizontal shift moves the graph of a function left or right without changing its shape.

Front

What is the effect of a vertical stretch on the graph of a function?

Back

A vertical stretch increases the distance between points on the graph and the x-axis.

Front

What is the effect of a vertical compression on the graph of a function?

Back

A vertical compression decreases the distance between points on the graph and the x-axis.

Front

How does a negative sign in front of a function affect its graph?

Back

A negative sign reflects the graph across the x-axis.