f(x) = x^4 - x^3 - 4^x2 +4 
 
By DesCartes' rule of signs it has 2 sign changes so it
has 2 or 0 positive real zeros.

We know by the factored form 

f(x) = (x^3 - 4x - 4)(x-1)

That it has at least 1 positive real zero, 1, so by DesCartes' 
rule of signs, it MUST have 2 positive real zeros. 

We know since 1 has multiplicity 1 that the curve cuts
through the x-axis there.

We know it goes up on the far right because the leading
coefficient 1 of 1x^4 is positive.  We know that it also goes 
up on the far left also because the degree 4 is even.


We make a table of 5 values:

 x | y
-2 | 12
-1 | 2
 0 | 4
 2 |-4
 3 |22 

We plot those points:




So the graph must look something like this:



Edwin