If there are three x-intercepts for a degree-4 polynomial, what must be true of the multiplicity of one of the zeroes?

If the polynomial is "up" on both ends, is the leading coefficient positive or negative?

Use this information to invent any polynomial you like that fits the requirements: three linear factors, one of which is repeated; and a positive leading coefficient.

If there are vertical asymptotes at x = 2 and at x = -1, what two factors must be in the denominator?

If the horizontal asymptote is at y = 1, then how must the degrees of the numerator and denominator compare, and how much their leading coefficients compare?

If y = x for x = 4, what must be a factor of the numerator?

If y = 2 when x = 0, then what must be the constant term of the numerator?

Use this to create a rational function which fits the requirements.

To learn how to set up and solve variation equations, tryhere.