Question

Write the equation of a function f(x) that has the following characteristics:Zero at x = 0 with multiplicity of 1Zero at x = 4 with multiplicity of 3Zero at x = -3 with multiplicity of 2Zero at x = 7 with multiplicity of 4Degree of 10Leading coefficient of -5Identify the end behavior of this function.

Answer 1

Zeroes

x=4 with a multiplicity of 3

zeroes make the function zero, so:

x-4 = 0

x = 4

Multiplicity is the power of the factor.

multiplicity of 3

(x-4)^3

For the rest:

x(x-4)^3 (x+3)^2 (x-7)^4

Degree of 10, leading coefficient of -5

The leading term is the term with the highest power, and its coefficient is the leading coefficient.

Add all the coefficients to obtain the degree 3+2+4+1 = 10

f(x) = -5x(x-4)^3 (x+3)^2 (x-7)^4