GRAPHS ON THE GO: Mod effect - 3

In this we are back again with one more effect of modulus which is very popular.

Now we need to know what  happens when modulus is applied to x only.

Now we need to understand what does it means,

it means that y = f(x) is changed to y = f(|x|).

This further means that for every negative value of x the output will be same as it was given for positive value of x because the -x will change to +x due to application of modulus function.

Now like always lets take an example-

y = x² - 3x + 2        (original)

y = |x|² - 3|x| + 2   (modified)

Now Lets see the graph of original one-

y = x² - 3x + 2 

Now when x is changed to |x| lets see what changes should occur to the graph.

Lets break modulus -

for x > 0

we get y = x² - 3x + 2 

for x < 0

we get y = (-x)² - 3(-x) + 2 

Now lets see the graph of case 1 and case 2-

CASE 1

CASE 2

 

Now as it is clear that graph of 1 gets reflected along y.

This proves that for positive and negative input of x the value of y will remain same.

On combining both the graphs we get-

y = |x|² - 3|x| + 2

A quick glimpse to how we can draw this kind of graph-

#Shortcut for f(x) to f(|x|)-

1. Take x>0 side and Delete the x<0 region graph.

2. Replicate x>0 region to x<0 region

3. You are done.

(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