Question

What value is a discontinuity of x squared plus 7 x plus 1, all over x squared plus 2 x minus 15?

x = -1

x = -2

x = -5

x = -4

Answer 1

Do you mean x^2 + 7x + 1 / x^2 + 2x - 15?

Answer 2

yes @KirbyLegs

Answer 3

If so, then you need to use reverse foil on the quadratic equations

x^2 + 7x + 1 / (x+5)(x-3)

Answer 4

It's whatever value of x causes the denominator to be zero.
In this case, you don't need to look at the numerator.
Just look at the denominator.
Plug in each choice of x into the denominator.
Whichever one makes the denominator zero is it.

Answer 5

Correct mathstudent. Look at the denominator and see where a term would equal 0
That signifies a discontinuity.

Answer 6

i tried what both of you told me but none of the choices give me zero. :/

Answer 7

There are actually two discontinuties

x+5 = 0
x = -5

x-3 = 0
x=3

x = -5 is one of the choices. That is the correct answer.

Answer 8

thank you @KirbyLegs

Answer 9

You're welcome

Answer 10

and thank you @mathstudent55

Answer 11

\(x^2 + 2x - 15\)

A. x = -1: \((-1)^2 + 2(-1) - 15 = 1 - 2 - 15 = -16\) This is not it.

B. x = -2: \((-2)^2 + 2(-2) - 15 = 4 - 4 - 15 = -15\) This is not it.

C. x = -5: \((-5)^2 + 2(-5) - 15 = 25 - 10 - 15 = 0\) THIS IS IT.

D. x = -4: \((-4)^2 + 2(-4) - 15 = 16 - 8 - 15 = -7\) This is not it..

As @KirbyLegs correctly pointed out above, there are actually two discontinuities in the denominator, but you can only choose one in your choices. It is x = -5.

Answer 12

why dont we look at the numerator? i was confuse on that one, can someon explain the WHY not look at the numerator please?

Answer 13

We look at the numerator and see that the numerator consists of the polynomial,
\(x^2 + 7x + 1\).

A polynomial contains no discontinuities. In other words, unless otherwise stated, the domain of a polynomial is all real numbers. Any number you plug in for x into this polynomial will give a y value. Even if the y value is zero for some x value, a zero in the numerator does not constitute a discontinuity. Zero divided by a non-zero number is perfectly acceptable. Since we can quickly conclude that about the numerator, we no longer need to think about it.

Then we focus our attention on the denominator. Once again it is a polynomial. Here we are concerned that for some value(s) of x, the y value will be zero. That is unacceptable because division by zero is undefined. That is what would cause a discontinuity.

Another typical source of discontinuities is a square root. If you had a square root in the numerator or denominator, you'd have to look at it because for real numbers, square root is defined only for non-negative numbers. A square root is a possible cause of a discontinuity, and whether it is in the numerator or denominator, it must be taken into consideration.