Function Transformations & Inverses

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 less than 1, causing the graph to be 'squished' towards the x-axis.

Front

Describe the transformation of the function h(x) = 1/5f(x).

Back

This represents a vertical compression by a factor of 1/5.

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

If f(x) = x^2, what is the transformation of g(x) = x^2 - 5?

Back

The graph of g(x) is the graph of f(x) shifted down 5 units.

Front

What does the transformation f(x) = (x - 3)^2 + 5 represent?

Back

This represents a right shift of 3 units and an upward shift of 5 units.

Front

What is the effect of adding a constant to the input of a function?

Back

Adding a constant to the input shifts the graph to the left if the constant is positive and to the right if it is negative.

Front

Describe the transformation of m(x) = f(x + 1).

Back

This represents a left shift of 1 unit.

Front

What is the relationship between the domain and range of a function and its inverse?

Back

The domain of the original function becomes the range of its inverse, and the range of the original function becomes the domain of its inverse.

Front

If f(x) has a domain of [2,∞), what is the domain of f^-1(x)?

Back

The domain of f^-1(x) is [3,∞) if the range of f(x) is [3,∞).

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, causing the graph to be 'stretched' away from the x-axis.