Answer:
option B and C
Step-by-step explanation:
Lets check each function
Lets simplify [tex]\frac{x^2-25}{x+5}[/tex]
factor the numerator
[tex]x^2-25 = (x+5)(x-5)[/tex]
[tex]\frac{(x+5)(x-5}{x+5}[/tex]
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 [tex]\frac{x^2+10x+25}{x+5}[/tex]
factor the numerator
[tex]x^2+10x+25 = (x+5)(x+5)[/tex]
[tex]\frac{(x+5)(x-5}{x+5}[/tex]
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
