Answer the following questions related to the concept of y-intercept of a polynomial graph:
a. (a) Define the y-intercept of the graph of a real polynomial function.
b. (b) For the general polynomial f(x)=anxn+an−1xn−1+⋯+a1x+a0, explain why the constant term a0 alone determines the y-intercept.
c. (c) The polynomial g(x)=5x4−7x2+9 is given. Justify, without performing any plotting, that the point (0,9) must lie on its graph.