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 it mean to reflect a function over the x-axis?

Back

Reflecting a function over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

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, making the graph taller.

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 between 0 and 1, making the graph shorter.

Front

How does the graph of f(x) = x^2 change when replaced with f(x) = (x - 3)^2?

Back

The graph shifts 3 units to the right.

Front

What is the effect of adding a constant to a function, such as f(x) + 2?

Back

Adding a constant shifts the graph vertically; in this case, it shifts the graph up by 2 units.

Front

What happens to the graph of f(x) when it is replaced with -f(x)?

Back

The graph is reflected over the x-axis.

Front

If f(x) = x^2, what is the transformation for g(x) = 0.5f(x)?

Back

This represents a vertical compression by a factor of 0.5.

Front

What does it mean to translate a function?

Back

Translating a function means shifting its graph horizontally and/or vertically without changing its shape.

Front

What is the parent function of a quadratic function?

Back

The parent function of a quadratic function is f(x) = x^2.