GRAPHS ON THE GO: f(x) to f(-x).

What happens when f(x) is transformed to f(-x)?

Let's take,                         y = f(x)        (original)

which changes to             y =  f(-x)     (modified)

What it means is that, when x > 0 the function takes negative input and hence gives result which was given by positive of original function and vice-versa.

Lets take an example of y = x + 1  which changes to y = -x + 1

x	y(original)	y(modified)
2	3	-1
-2	-1	3
5	6	-4
-5	-4	6

Form this table we can extract that the values of  y changes,

it means that,

original graphs values for x>0 must be equal to x<0 values of modified one.

and

original graphs values for x<0 must be equal to x>0 values of modified one.

Lets see what the change in graph happens.

y = x + 1

y = -x + 1

Now from the graph formed our predictions are proved to be correct.

#Shortcut to this transformation-

Just rotate the y axis 180deg

or

Reflect each region of  x in y and remove the previous one.

Now just a quick glimpse to this-

(Image credits- https://www.desmos.com/)

Stay Tuned for the next post.

For any query comment down there.

#graphs_on_the_go  #understanding_graphs #mathematics, #feed-o-math , #quadratic_equations