Question

When looking at the rational function f of x equals the quantity x minus one times the quantity x plus two times the quantity x plus four all divided by the quantity x plus one times the quantity x minus two times the quantity x minus four , Sue and Ed have two different thoughts. Sue says that the graph of the function has zeros at x = −1, x = 2, and x = 4. Ed says that the function is undefined at those x values and discontinuities are created in the graph . Who is correct? Justify your reasoning by explaining the difference between zeros and discontinuities.

Answer 1

Answer: Function has zeros at x=-1

Explanation: According to the question the function will be f(x)= $\frac{x-x+2x+4}{x+x-2x-4}$ ⇒f(x)= $\frac{2x+4}{-4}$⇒ f(x) =$\frac{-x-2}{2}$

Since, we can replace f(x) by another dependent variable y.

Thus, the function can be write y = $\frac{-x-2}{2}$

since we know that zeros are the points which give the value zero after substituting in the function while discontinuities are the points in which function is not continues.

Here it is an equation of line which is only have zero at x=-1 . And the line can't have any discontinuities.