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Graphical Transformation (involve modulus) - (Concept)
$
f(x) \rightarrow|f(x)|
$
When $y=f(x)$ given
Leave the positive part of $f(x)$ (the part above the $x$-axis) as it is
Now, take the image of the negative part of $f(x)$ (the part below the $x$-axis) about the $x$-axis.
OR
Take the mirror image in the $x$-axis of the portion of the graph of $f(x)$ which lies below the $x$-axis
For Example:
y=x3 y=|x3| y=|x3| and y=x3
Transformation $\mathrm{f}(\mathrm{x}) \rightarrow \mathrm{f}(|\mathrm{x}|) \mid$
When $y=f(x)$ given
Leave the graph lying right side of the $y$-axis as it is
The part of $f(x)$ lying on the left side of the $y$-axis is deleted.
Now, on the left of the $y$-axis take the mirror image of the portion of $f(x)$ that lying on the right side of the $y$-axis.
For Example:
y = f(x) y = f(x) and y = f(|x|) y = f(|x|)
Transformation $\mathrm{f}(\mathrm{x}) \rightarrow|\mathrm{f}(|\mathrm{x}|)|$
First $\mathrm{f}(\mathrm{x})$ is transforms to $|\mathrm{f}(\mathrm{x})|$
Then $|f(x)|$ transforms to $|\mathrm{f}(|\mathrm{x}|)|$
Or
(i) $f(x) \rightarrow|f(x)| \quad$ (ii) $f(x) \rightarrow f(|x|) \mid$
For Example:
y = f(x) y = |f(x)| y = f(|x|)
y = |f(|x|)|
$\begin{aligned} & y=f(x) \rightarrow|y|=f(x) \\ & y=f(x) \text { is given }\end{aligned}$
Remove the part of the graph which lies below X-axis
Plot the remaining part
take the mirror image of the portion that lies above the x-axis about the x-axis.
| Exam | Chapter |
| JEE MAIN | Sets, Relations and Functions |
The area bounded by the lines $y=||x-1|-2|$ and $\mathrm{y}=2$ is
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The number of elements in the set $\left \{ x\epsilon \mathbb{R}:\left ( \left | x \right | -3\right ) \left | x+4 \right |=6\right \}$ is equal to :
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Which of the following is the graph of $|y|=\cos x$?
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The number of solutions of $|\cos x|=\sin x$, such that $-4 \pi \leq x \leq 4 \pi$ is :
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Let $f(x)=\left|2 x^2+5\right| x|-3|, x \in R$. If $m$ and $n$ denote the number of points where $f$ is not continuous and not differentiable respectively, then $m+n$ is equal to:
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If the graph of $y=f(x)$ is as shown below then the graph of $y=f(|x|)$ is
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If the graph of $y=x^{2}-3x+2$ is
then the graph of $y=||x^2|-3|x|+2|$ is
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Which of the following is the graph of $y=\frac{1}{2} \cos x$ ?
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Which of the following is the graph of $y=4^{-x}$?
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Let $\mathbb{R}$ be the set of real numbers and $f: \mathbb{R} \rightarrow \mathbb{R}_{\text {be given by }} f(x)=\sqrt{|x|}-\log (1+|x|)$ We now make the following assertions:
I. There exists a real number $A$ such that $f(x) \leq A_{\text {for all } x \text {. }}$.
II. There exists a real number such that $f(x) \geq B$ for all $x$.
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