Sketch the graph of f(x)

Question

So I have been really struggling trying to figure this out. I guess I am just really trying to find what the graph of f(x) looks like. Because I have to graph these equations:

y=f(x-2)

y=f(x)-2

y=-2f(x)

y=f(-2x)

I know for the first one it would be f(x) shifted 2 to the right and the second one would be f(x) shifted down 2. But I can't figure out what y=f(x) graphs out to be. I tried to look up pictures of it online and some show just a linear line or a quadratic U shape. Others have more curves so I need help graphing these :/

Answer 1

f(x) could be anything. If the problem doesn't tell you what f(x) is, then all they want is for you to state what the various transforms would do to the graph of any function f(x). The transforms will do the same thing to every graph.

 

For instance, as you stated, f(x-2) shifts the graph of f(x) two places to the right along the x-axis.  If f(x) is a parabola, it shifts the parabola two places to the right. If f(x) is a straight line, it shifts the line two places to the right.  If f(x) is some weird rational function with asymptotes, it will shift the whole graph and its asymptotes 2 places to the right.