Explanation:
a)
high positive x (x going to +infinity) would create high positive y (also +infinity).
while high negative x (x going to -infinity) would create high negative y (also -infinity), x⁵ with its odd exponent is negative for negative x and positive for positive x.
the graph is showing just the opposite behavior.
so, it cannot be the right graph.
b)
the degree of the polynomial is the highest exponent of the input variable x. in our case : 5
a polynomial of degree n must have n zeros (or roots).
in our case we need 5 zeros. but there are only 3. no matter how we shift it up or down, the x-axis will not intercept it more than 3 times.
so it cannot be the right graph.