Write a rational function g with vertical asymptotes at x = 3 and x = -3, a horizontal asymptote at y = -4 and with no x-intercept.

Explanation

To write a rational function \( g(x) \) that meets the specified conditions, we will follow these steps:

### Step 1: Identify the vertical asymptotes
Given vertical asymptotes at \( x = 3 \) and \( x = -3 \), the denominator of the rational function must include the factors \( (x - 3) \) and \( (x + 3) \). Thus, we can express the denominator as:
\[ D(x) = (x - 3)(x + 3) = x^2 - 9 \]

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