Function Notation Transformations Check Point

Front

What is function notation?

Back

Function notation is a way to represent functions in mathematics, typically using symbols like f(x) to denote the output of a function f for a given input x.

Front

How do you represent a horizontal shift to the right in function notation?

Back

A horizontal shift to the right is represented as f(x - h), where h is the number of units shifted.

Front

What does f(x + 3) represent in terms of transformations?

Back

f(x + 3) represents a horizontal shift of the graph of f(x) to the left by 3 units.

Front

What is the effect of replacing f(x) with -f(x)?

Back

Replacing f(x) with -f(x) reflects the graph of the function across the x-axis.

Front

If f(x) = x^2, what is the transformation of f(x) when it is replaced with f(-x)?

Back

Replacing f(x) with f(-x) reflects the graph of the function across the y-axis.

Front

What does a vertical stretch by a factor of 2 mean for the function f(x)?

Back

A vertical stretch by a factor of 2 means that the output values of the function are multiplied by 2, making the graph taller.

Front

How do you express a vertical compression by a factor of 1/5 in function notation?

Back

A vertical compression by a factor of 1/5 is expressed as f(x)/5 or (1/5)f(x).

Front

What is the vertex of the function g(x) = f(x + 2) if the vertex of f(x) is (-4, 5)?

Back

The vertex of g(x) = f(x + 2) is (-6, 5), indicating a horizontal shift to the left by 2 units.

Front

What transformation occurs when f(x) is replaced with f(2x)?

Back

Replacing f(x) with f(2x) results in a horizontal compression by a factor of 1/2.

Front

What does the notation f^(-1)(x) represent?

Back

f^(-1)(x) represents the inverse function of f(x), which undoes the effect of the original function.