Transformations of Functions

Front

What is a transformation of a function?

Back

A transformation of a function refers to the changes made to the graph of the function, including translations, reflections, stretches, and compressions.

Front

What does it mean to translate a function?

Back

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

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

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

Back

Reflecting a function over the x-axis means flipping the graph upside down, changing the sign of the output values.

Front

How does the function y = -2|x| transform from y = |x|?

Back

The function y = -2|x| is stretched vertically by a factor of 2 and reflected over the x-axis.

Front

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

Back

Adding a constant to a function translates the graph vertically. For example, f(x) + c shifts the graph up by c units.

Front

What is the effect of subtracting a constant from a function?

Back

Subtracting a constant from a function translates the graph vertically down. For example, f(x) - c shifts the graph down by c units.

Front

What does the transformation g(x) = (x - 1)^3 represent if f(x) = x^3?

Back

The transformation g(x) = (x - 1)^3 represents a horizontal translation of the graph of f(x) = x^3 to the right by 1 unit.

Front

What is the transformation of the function g(x) = -√x?

Back

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