Question

Which statement correctly uses limits to determine a vertical asymptote of g (x) = StartFraction negative 7 (x minus 5) squared (x + 6) Over (x minus 5) (x + 5) EndFraction There is a vertical asymptote at x = 5, because Limit of g (x) as x approaches 5 minus = infinity and limit of g (x) as x approaches 5 plus = negative infinity There is a vertical asymptote at x = 5, because Limit of g (x) as x approaches 5 minus = negative infinity and limit of g (x) as x approaches 5 plus = infinity There is a vertical asymptote at x = –5, because There is a vertical asymptote at x = –5, because

Answer 1

Vertical asymptote concept used to solve this question. First, I explain the concept, and then, you use it to solve the question.

Using this, we get that the correct option is:

There is a vertical asymptote at x = –5, because limit of g(x) as x approaches -5 minus = negative infinite and limit of g(x) as x approaches -5 plus, it is positive inifnite.

Vertical asymptote:

A vertical asymptote is a value of x for which the function is not defined, that is, it is a point which is outside the domain of a function;

In a graphic, these vertical asymptotes are given by dashed vertical lines.

An example is a value of x for which the denominator of the function is 0, and the function approaches infinite for these values of x.

The fraction is:

$g(x) = -\frac{7(x-5)^2(x+6)}{(x-5)(x+5)}$

Simplifying:

The term (x-5) is present both at the numerator and at the denominator, and thus, the function can be simplified as:

$g(x) = -\frac{7(x-5)(x+6)}{x+5}$

Vertical asymptote:

Point in which the denominator is 0, so:

$x + 5 = 0$

$x = -5$

Now, we take a look at the graphic of the simplified function, given at the end of this answer.

You can see that as x approaches -5 to the left, that is -5 minus, the function goes to minus infinite, and as x approaches -5 to the right, that is, -5 plus the function goes to plus infinite, and thus, the correct answer is:

There is a vertical asymptote at x = –5, because limit of g(x) as x approaches -5 minus = negative infinite and limit of g(x) as x approaches -5 plus, it is positive inifnite.

For another example of vertical asymptotes, you can check brainly.com/question/24278113

Answer 2

Answer:

D

Step-by-step explanation:

edge i graphed it on desmos