Question

Determine whether or not the function is continuous for the given values of X.

Answer 1

Answer:

A. ​Yes, the point is​ defined, ​limit f(x) exists, and ​limit f(x) 0.

Step-by-step explanation:

Let be $f(x) = \frac{x^{2}-25}{x-7}$, a rational function is continuous at a value of $x$ if and only if denominator is different from zero. In particullar, $x-7 \neq 0$.

Then, we find that function is continuous for every value of $x$ except $x = 7$. Thus, the function is continuous at $x = 0$, which is evaluated below:

$f(x) = \frac{(x+5)\cdot (x-5)}{x-7}$

$f(0) = \frac{(0+5)\cdot (0-5)}{0-7}$

$f(0) = \frac{(5)\cdot (-5)}{-7}$

$f(0) = \frac{-25}{-7}$

$f(0) = \frac{25}{7}$

Thus, correct answer is A.