How does a transformation affect the graph of f(x) if it is changed to:
a) f(x) + 2
b) f(x - 3)

If you add a value to the outcome of the function (as in case a), you will just shift the graph up along the y-axis. Makes sense, right, since you're adding an extra 2 to the value you will plot on the y axis.

If you subtract (in this example) a value to the input of the function, you're actually "looking back" into the past of the graph (i.e., the left side). For example, for x=4 you're now plotting the value that used to be at x=1. So this shifts the graph to the right.

That may be confusing at first. But I hope with a little thought experiment, you get it.

Sin a = cos b

sin a = sin (90-b)

a =90-b

a+b =90,

From angle sum property, we know that

In a triangle, a + b + c =180

90+c =180

c =90°.

Now cos90° = 0.

Therefore, cosc =0

Hope this helps!