Question

Which of the following represents a function that passes through the point x = a and "bounces off" the point x = b, and has a a degree of 5?A. y = (x - a)(x - b)^4B. y = (x - a)72(x - b)^2(x - c)C. y = (x - a)^2(x - b)^3D. y = (x - a)(x - b)^2E. None of These

Answer 1

ANSWER;

`y=(x-a)(x-b)^4`

EXPLANATION;

Here, we want to get the equation of the function

From the question, we have that the function is of degree 5. What this mean is that it is expected to have 5 roots which may (with multiplicities) or may not be the same

From the question, we have x = a as a root, with a bounce off at x= b

This mean these two points are the roots

To bounce off simply mean to touch and change direction

Thus, it means to have touched and bounced off b, b is of the bigger multiplicity with the multiplicity of a being one only

Thus, in the factored form, we have the function as;

`y=(x-a)(x-b)^4`