Question

question 4 (multiple choice worth 5 points) (04.02r mc) what value is a discontinuity of \\(\frac{x^2 + 5x + 2}{x^2 + 2x - 35}\\)? \\(x = -5\\) \\(x = -7\\) \\(x = -2\\) \\(x = -1\\)

Explanation:

Step1: Find denominator roots

To find discontinuities, set the denominator \(x^2 + 2x - 35 = 0\). Factor the quadratic: \(x^2 + 2x - 35=(x + 7)(x - 5)=0\).

Step2: Solve for x

Set each factor to zero: \(x + 7 = 0\) gives \(x=-7\); \(x - 5 = 0\) gives \(x = 5\). From the options, \(x=-7\) is a root of the denominator, so it's a discontinuity.

Answer:

\(x=-7\) (corresponding to the option with \(x = -7\))