# Gre.al.12 transformationof a function

• MHB
• karush
In summary, the graph of $y=\left|x-6\right|$ is a transformation of $y=\left|x\right|$ with a translation of 6 units to the right. It can also be visualized by sketching the graph of $y=x-6$ and reflecting the part below the x-axis above the x-axis. This method works for any absolute value function.
karush
Gold Member
MHB
$\tiny{gre.al.12}$
The graph of $y=\left|x-6\right|$
is is the standard $(x,y)$ coordinate plane.
Which of the following transformations. when applied to the graph of
$y=\left|x\right|$, in the graph of $y=\left|x-6\right|$?

a. Translation to the right 6 coordinate units
b. Translation to the left 6 coordinate units
c. Translation up 6 coordinate units
d. Translation down 6 coordinate units
e. Reflection across the line $x=6$

ok chose a. Translation to the right 6 coordinate units
since we are only talking about changes in x and the minus sign will move the graph to the right

well probably a better way to explane this

Think of $|x-6|$ as the distance (note distance is always $\ge$ zero) between $x$ and $6$ ...

$x=6 \implies |6-6| = 0$, the vertex of the transformed function $y = |x|$,hence the horizontal shift to the right.Another way to visualize the transformation is to sketch the graph of $y = x - 6$, and reflect the part of the graph below the x-axis above the x-axis ...

btw, this graphing method works with any real-valued absolute value function

i used the abs on desmos to ck it
but i think many people transform the wrong direction by impulse

## 1. What is a "Gre.al.12 transformation of a function"?

A "Gre.al.12 transformation of a function" is a type of mathematical operation that involves changing the shape, position, or orientation of a graphed function. This transformation is usually denoted by adding a set of numbers, known as coefficients, to the original function.

## 2. What types of transformations can be applied to a function using Gre.al.12?

Gre.al.12 transformations can include translations, reflections, dilations, and combinations of these operations. These transformations can change the position, size, and shape of the original function's graph.

## 3. How do I perform a Gre.al.12 transformation on a function?

To perform a Gre.al.12 transformation on a function, you will need to identify the coefficients for the desired transformation. These coefficients will determine the type and amount of transformation to be applied. Then, simply apply the coefficients to the original function and graph the new transformed function.

## 4. What is the purpose of performing a Gre.al.12 transformation on a function?

The purpose of a Gre.al.12 transformation is to manipulate the graph of a function in order to better understand its behavior and characteristics. These transformations can also be used to solve equations and inequalities involving functions.

## 5. Are there any limitations to performing a Gre.al.12 transformation on a function?

While Gre.al.12 transformations can be applied to a wide range of functions, there are some limitations. For example, some transformations may result in undefined or imaginary values, and others may not be possible for certain types of functions. It is important to carefully consider the characteristics of the original function before applying a Gre.al.12 transformation.

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