Transformation of Graphs-I

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We are going to learn following transformation:

y = f(x)

1. - f(x)

2. f(-x)

3. f(|x|)

4. |f(x)|

5. f(x + a)

6. f(x - a) 

7. f(x) + a

8. f(x) - a

9. f(ax)

10. af(x)

Students are requested to understand these transformations carefully.



1. f(x) \to - f(x)

 Take the symmetry about x-axis and do not consider the original graph.
(As negative value of function become positive and positive values become negative)







2. f(x) \to f( - x)

 Take the symmetry about y-axis and do not consider the original graph.
(As value on negative value of 'x' now becomes the value on positive value of 'x' and vice-versa.)

SEE CAREFULLY THE DIFFERENCE BETWEEN f(x) = - [x] and f(x) = [-x]





3. f(x) \to f(|x|)

 Do not consider negative x-axis portion of graph and then take the symmetry about y-axis.
(As positive side of x-axis and negative side of x-axis have the same graph)





4. f(x) \to |f(x)|

 First take the symmetry about below portion of x-axis graph about x-axis and then do not consider ONLY the below portion of x-axis graph.
(As value of |f(x)| will always be positive and no portion of graph will be below the x-axis)







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