Rather than graphing it would be better, in general, to think about what "surjective" and "injective"mean.

"Surjective", also called "onto", just means that f(x) takes on every possible value- which is the same as saying we can solve the equation for all y. Here, we would solve by:

1) subtract from both sides:

2) multiply both sides by -1:

3) take the logarithm of both sides:

4) multiply both sides by -1:

Now, can we do that forally? The only possible problem is with that logarithm. log(x) is only defined for x> 0 so we must have which means .

No, this function is NOT surjective onallreal numbers. Its value is never larger than .

"Injective", also called "one-to-one", means that twodifferentvalues of x must givedifferentvalues of f(x) so you need to ask "is it possible to have f(x)= f(y) without x=y?"

Look at .

The obvious first step is to subtract from both sides from both sides:

Now multiply both sides by -1: 2^{-x}= 2^{-y}

Take the logarithm of both sides: -xlog(2)= -ylog(2)

Finally, divide both sides by -log(2): x= y.

That says that if f(x)= f(y), then we must have x= y. Yes, this function is injective.