graph of f(x)

Question

I am still having trouble trying to figure out how to graph functions. I was given a graph that is f(x) and it says it has a domain of [-4,4]. I then had to make four graphs:

y=f(x-2)

y=f(x)-2

y=-2f(x)

y=f(-2x)

So I know for the first one it is just f(x) shifted right 2 so I redrew the graph moved over. Then the second one is just f(x) shifted down 2 so I did the same thing and redrew it. But I am stuck on the last two. I know y=-2f(x) is flipped because it is negative and then it expands because it is scaled vertically by a factor of 2. I also know y=f(-2x) shrinks and I think it is scaled horizontally by a factor of -1/2. I am unsure of how to graph these still. The other ones I just moved over or down and I am confused as to how to graph the last two. Please help :/

Answer 1

To help with the third one, let's try to flip the problem around and isolate the X so that you can see it from another angle. So then we have:

 Y =  -2f(X)

---    -------

-2       -2

 

Simplified, it looks like:

-(1/2) Y = f(x)   or   f(x) = -(1/2) Y.

 

This way, you can see For every 1 additional numbers you put one more number into X, Y decreases by two

1 = -1/2 * -2  (1, -2)

2 = -1/2 * -4  (2, -4)

 

As for the fourth problem, it does move in half, so then, if X is two what is half of two and turned negative? if X is four, what is half of four and negative? (Remember, the graph equation has a negative sign attatched to it).