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 are the four main types of transformations?

Back

The four main types of transformations are translation, reflection, dilation, and rotation.

Front

What is a translation in the context of function transformations?

Back

A translation is a transformation that shifts a graph horizontally and/or vertically without changing its shape.

Front

What does a reflection do to a function's graph?

Back

A reflection flips the graph of a function over a specified axis, such as the x-axis or y-axis.

Front

What is dilation in function transformations?

Back

Dilation is a transformation that stretches or compresses the graph of a function vertically or horizontally.

Front

How does the equation f(x) = x^2 change when translated right by 2 units?

Back

The new equation is f(x) = (x - 2)^2.

Front

What is the effect of the transformation g(x) = f(x) + 3?

Back

This transformation translates the graph of f(x) vertically upward by 3 units.

Front

If f(x) = √x, what is the reflection over the x-axis?

Back

The reflected function is g(x) = -√x.

Front

What is the domain of the function f(x) = √x?

Back

The domain is [0, ∞).

Front

What does the notation g(x) = (x + 1)^3 represent?

Back

This represents a horizontal translation of the parent function f(x) = x^3 to the left by 1 unit.