Transformations of Functions

Front

What is a transformation of a function?

Back

A transformation of a function is an operation that alters the graph of the function in some way, such as shifting, reflecting, stretching, or compressing.

Front

What does shifting a function to the right by 2 units look like?

Back

The transformation of the function f(x) to g(x) = f(x - 2) shifts the graph of f(x) to the right by 2 units.

Front

What is the effect of a negative sign in front of a function?

Back

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

Front

How do you represent a vertical shift of a function?

Back

A vertical shift of a function f(x) by k units is represented as g(x) = f(x) + k.

Front

What does the equation g(x) = (x + 3)^2 represent?

Back

The equation g(x) = (x + 3)^2 represents a horizontal shift of the graph of f(x) = x^2 to the left by 3 units.

Front

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

Back

The transformation g(x) = -f(x) reflects the graph of f(x) across the x-axis.

Front

What does the equation g(x) = f(x) + 5 indicate?

Back

The equation g(x) = f(x) + 5 indicates a vertical shift of the graph of f(x) upwards by 5 units.

Front

What is the effect of the transformation g(x) = f(x - 4)?

Back

The transformation g(x) = f(x - 4) shifts the graph of f(x) to the right by 4 units.

Front

How do you identify a vertical stretch of a function?

Back

A vertical stretch of a function f(x) by a factor of a (where a > 1) is represented as g(x) = a * f(x).

Front

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

Back

The transformation g(x) = f(-x) reflects the graph of f(x) across the y-axis.