Question

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

Answer 1

Do you have a calculator?

Answer 2

yes

Answer 3

Take each of the choices and plug it in for x

Answer 4

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

Answer 5

im confused why would i do that?

Answer 6

ok... you said you have a calculator what is the value of

\[10 \div 0 = ?\]

Answer 7

there is no value

Answer 8

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....

Answer 9

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

Answer 10

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..?

Answer 11

ok