Determine the interval(s) for which the function is continuous.
$f\left(x\right)=x^2+4x-12$

• A. $(-\infty ,-12),(-12,\infty )$
• B. $(-\infty ,-6),(-6,2),(2,\infty )$
• C. $(-\infty ,\infty )$

Answer: (C)

Verified step by step guidance

1. Identify the type of function given. The function f(x) = x^2 + 4x - 12 is a polynomial.
2. Recall that polynomial functions are continuous everywhere on the real number line. This means they do not have any breaks, holes, or jumps.
3. Since f(x) is a polynomial, it is continuous for all x in the real numbers.
4. Therefore, the interval of continuity for f(x) is (-∞, ∞).
5. Conclude that the function is continuous over the entire real line, confirming the interval (-∞, ∞).