How to solve this graphical function transfromation problem?

Question

How to solve problems like this.

I always face problem in solving function transformation related problems.

Is there any good way to solve problems like this..

Answer 1

You could think of it in this way

1. If the modification is in the form $y=f(x)+a$, then the graph shifts up/down by $a$.
2. If the modification is in the form $y=f(x+a)$, then the graph shifts left/right by $-a$. (Take note of the negative sign here. So for example, if we have $y=f(x-2)$, then the graph shifts to the right by 2 units.
3. If the modification is in the form $y=a \cdot f(x)$, then the graph is stretched vertically by a factor of $a$.
4. If the modification is in the form $y=f(a \cdot x)$, then the graph is stretched horizontally by a factor of $\frac{1}{a}$. (So for example if we have $y=f(2x)$, then the graph is "compressed" by half.)

Most of the questions you encounter should be a combination of the above.

All the best.