can someone help me with this question please?

[ally1784]

It'll be great if someone can assist me with this

[fun_jirachi]

I can do the question, but it defeats the purpose of whatever this work is for (looks like tutoring work?).

So let me ask some questions in response (that really, you should be noting in any question you ask here):
- What have you tried?
- What do you know about transforms?
- Do you have any ideas on what your first step could be?

[ally1784]

I know I have to write out the dilation, translation, and reflection.

[fun_jirachi]

In general:

\(f(x-a)\) shifts the function \(f(x)\) \(a\) units in the positive x direction
\(f\left(\frac{x}{a}\right)\) dilates the function \(f(x)\) horizontally by a factor of \(a\)
\(af(x)\) dilates the function \(f(x)\) vertically by a factor of \(a\)
\(f(x) + a\) shifts the function \(f(x) a\) units in the positive y direction
\(f(-x)\) reflects the function in the y-axis, while \(-f(x)\) reflects the function in the x-axis. In some way, you can technically consider them as a dilation in either the x or y direction.

Note for a sequence of changes that involves some combination of the above, order is very important.
For example, dilating a function \(f(x)\) by a factor of \(\frac{1}{2}\) then shifting it four units to the right will yield a different function than doing those steps in the reverse direction. A decent order to follow is shift in the x-direction, dilate in the x-direction, dilate in the y-direction, shift in the y-direction (though this may not be immediately helpful in some situations). Note also that reflection can technically be considered as 'dilation' given the way reflection works from the above tips, and as such can and should be applied in the same step. Working backwards may also be helpful.