Question

The Figure above shows the graphs of five functions, distinguished by color. For every function, enter below the letter p if the graph may be that of a polynomial, and the letter n if it cannot be the graph of a polynomial. (Of course we assume that figure shows all the relevant aspects of the graph.)

Answer 1

The following is a breakdown of whether the graph of each function may be that of a polynomial:

Blue No (n)

Green Yes (p)

Purple (magenta) No (n)

Red Yes (p)

Yellow No (n)

Blue: The blue graph has a vertical asymptote at x = -1. Polynomials do not have vertical asymptotes.

Green: The green graph is a smooth curve that passes through the origin. It is possible for a polynomial to have these properties, so the green graph may be that of a polynomial.

Purple (magenta): The purple graph has a hole at x = -2. Polynomials do not have holes, so the purple graph cannot be that of a polynomial.

Red: The red graph is a straight line. Polynomials can be straight lines, so the red graph may be that of a polynomial.

Yellow: The yellow graph has a horizontal asymptote at y = 1. Polynomials do not have horizontal asymptotes.