Q. How to Left shifts and right shifts a graph?

Ans.

When you're translating (shifting) a graph, it's easy to get subtracting and adding mixed up. It seems counter-intuitive that subtracting causes motion in the positive direction, while adding causes motion in the negative direction. If you want to understand this strange phenomenon, try this experiment:

plot the graphs of

y = x² and y= (x- 1) ²

by hand. What happens?

As with translation, scaling seems to run counter-intuitively. Multiplication of the variable by a number will cause shrinking, while division of the variable by a number causes expansion.