Final answer:
The interval where the function y = x² - 5x - 36 is positive is (-∞, -4) ∪ (9, ∞).
Step-by-step explanation:
To identify the interval(s) where the function y = x² - 5x -36 is positive, we need to determine the values of x for which the function's output, y, is greater than zero.
To do this, we can set up a sign chart. First, let's factor the quadratic equation: y = (x - 9)(x + 4).
We can see that the function is positive when x is greater than 9, or when x is less than -4. Therefore, the interval where the function is positive is (-∞, -4) ∪ (9, ∞).