Final answer:
The vertical asymptotes of the function f(x) = 2/(x^2 + 3x - 10) are at x = -5 and x = 2, which are found by factoring the denominator and setting each factor equal to zero.
Step-by-step explanation:
To identify the vertical asymptotes of the function f(x) = \frac{2}{{x^2 + 3x - 10}}, we need to determine the values of x for which the denominator is zero, as these are the values where the function is undefined and the graph of the function can have vertical asymptotes.
First, let's factor the denominator:
x^2 + 3x - 10 = 0
This is a quadratic equation, and it can be factored as:
(x + 5)(x - 2) = 0
Now, we can solve for x by setting each factor equal to zero:
- x + 5 = 0 → x = -5
- x - 2 = 0 → x = 2
Therefore, the vertical asymptotes of the function are at x = -5 and x = 2.