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Home > Graphical transformation (f(x) transforms f(ax) and f(x/a))

Graphical transformation (f(x) transforms f(ax) and f(x/a)) - (Concept)

$f(x)$ transforms to $f(a x) \quad(a>1)$
Shrink the graph of $f(x)$ 'a' times along the $x$-axis after drawing the graph of $f(x)$,
$f(x)$ transforms to $f(x / a) \quad(a>1)$
Stretch the graph of $\mathrm{f}(\mathrm{x})$ ' a ' times along the x -axis after drawing the graph of $\mathrm{f}(\mathrm{x})$,
For Example: The graph of $f(x)=\sin x, f(x)=\sin (2 x)$, and $f(x)=\sin (x / 2)$.

Transformation $\mathrm{f}(\mathrm{x}) \rightarrow \mathrm{f}(-\mathrm{x})$,
When we multiply all inputs by -1 , we get a reflection about the $y$-axis
So, to draw $\mathrm{y}=\mathrm{f}(-\mathrm{x})$, take the image of the curve $\mathrm{y}=\mathrm{f}(\mathrm{x})$ in the y -axis as a plane mirror $f(x) \rightarrow-f(x):$

When we multiply all the outputs by -1 , we get a reflection about the x -axis.
To draw $y=-f(x)$ take an image of $f(x)$ in the $x$-axis as a plane mirror
For example
The graph of $y=e^x, y=-e^x \quad$ (Transformation $\left.f(x) \rightarrow-f(x)\right)$

Exam Chapter
JEE MAIN Sets, Relations and Functions
Differential Calculus (Arihant)
Page No. : 205
Line : 10

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