Question

Given the function R(x)=x−4 / x+9, find the values of x that make the function less than or equal to zero. Write the solution in interval notation.

Answer 1

x ∈ (-9, 4]

Explanation:

The function changes sign where the binomial expressions change sign, at x = 4 and x = -9. For x > 4, both signs are positive. The signs will be different for -9 < x < 4. When the signs are different, the value of the function is negative, less than zero.

The function will be equal to zero at x = 4. There is a vertical asymptote at x = -9, so there is no zero at that point.

R(x) ≤ 0 for x ∈ (-9, 4].