Question

Which functions are continuous at x= -5? Select all that apply.

Answer 1

Answer:

The correct ones i belive are B and C

Answer 2

Answer:

option B  and C

Step-by-step explanation:

Lets check each function

 Lets simplify $\frac{x^2-25}{x+5}$

factor the numerator

$x^2-25 = (x+5)(x-5)$

$\frac{(x+5)(x-5}{x+5}$

Cancel out x+5  so we are left with x-5

When x=-5  then f(x) = x-5= -5-5 = -10

To make the function continuous at x=-5  the value of f(x) should be -10

So option B is correct

Now we check with option C  and D

Lets simplify $\frac{x^2+10x+25}{x+5}$

factor the numerator

$x^2+10x+25 = (x+5)(x+5)$

$\frac{(x+5)(x-5}{x+5}$

Cancel out x+5 , so we are left with x+5

When x=-5  then f(x) = x+5= -5+5 = 0

To make the function continuous at x=-5  the value of f(x) should be 0

So option C is correct