The polynomial function  f(x) = 5x5  + 3x  – 3 is graphed below. which statement  best  describes the root of  f(x) at point  p? a)the root at point p may be 3/5.b)the root at point p may be 1/5.c)the root at point p may be 5/3.d)the root at point p may be 1/3.

The roots of f(x) are the values for x at which f(x)=zero. The root of f(x) at point P is a bit redundant, since point P is the root of the function (and based on the graph, the only root). 

We could plug zero in for f(x) to find the value of x at Point P, but based on the graph/options provided and the complexity of the function, it may be easier to just eyeball the graph to get the correct answer. We see that point P is between 1/2 and 1 on the x-axis. 

Of the options provided, we want the value for x that satisfies: 1/2 < x < 1

a) 1/2 < 3/5 < 1     CORRECT ANSWER
b) 1/5 < 1/2           INCORRECT 
c) 5/3  > 1             INCORRECT
d) 1/3  < 1/2          INCORRECT