Barrelracing one year ago What are the discontinuities of the function f(x) = the quantity of x squared plus 5 x plus 6, all over 2 x plus 16.? a) x= -3 b) x = -2 c) x =-8 d) x = -5

1. anonymous

Do you have a calculator?

2. Barrelracing

yes

3. anonymous

Take each of the choices and plug it in for x

4. campbell_st

so the problem is $\frac{x^2 + 5x + 6}{2x + 16}$ so you just need to solve the denominator 2x + 16 = 0 you can't divide anything by zero so you need to find the value of x that makes the denominator zero that is the discontinuity

5. Barrelracing

im confused why would i do that?

6. campbell_st

ok... you said you have a calculator what is the value of $10 \div 0 = ?$

7. Barrelracing

there is no value

8. campbell_st

if you did the calculation you probably got a response like Math Error which means an answer doesn't exist... so a discontinuity is where part of the curve doesn't exist. so to find the discontinuity in this question you need to find the value of x that makes the denominator zero....

9. campbell_st

here is a graph of the cruve... the vertical dotted line is called an asymptote, it is a discontinuity... as you may see the curve doesn't cross the line. the value of the discontinuity is the the value of x that makes the denominator zero

10. campbell_st

so as I said earlier to find the discontinuity you need to solve 2x + 16 = 0 and that value of x is the discontinuity or you could plug all 4 choices into a calculator and then find the one that gives math error which is easier..?

11. Barrelracing

ok