Question

just need the letter choice answer don't need the explanation thanks,

Answer 1

correctTo find the corresc answer, lets examine the following:

1° - the function has an asymptote at x = -2.

It means that the function can not be defined for x = -2.

For option a)

$y(-2)=\frac{1}{-2-2}=-\frac{1}{4}$

a) is defined, so it is wrong!

for option b)

$y(-2)=\frac{2}{(-2)^2-4}=\frac{2}{4-4}=\frac{2}{0}=undefined$

It can be b).

Lets analyse that x = 0 -> in a value positive between 1 and 2. For option b), we have:

$y(0)=\frac{2}{0-4}=-\frac{1}{2}$

it is negative, and the expected value was positive.

b) is wrong!!

For c), lets analyze x = -2

$y(-2)=\frac{3}{-2+2}=\frac{3}{0}=\text{undefined}$

Now anallyzing x = 0:

$y(0)=\frac{3}{0+2}=1.5$

it is between 1 and 2, positive as we expected.

Lets check option d), for x = -2:

$f(-2)=-\frac{3}{2\times(-2)+4}=-\frac{3}{0}=\text{undefined}$

If we analyse it for x = 0, we have:

$y(0)=-\frac{3}{2\times0+4}=-\frac{3}{4}$

It is negative, and for this reason, different from the graph!

d) is wrong!

Analysing e) for x = -2

$y(-2)=\frac{1}{(-2)^2+2\times(-2)+1}=\frac{1}{4-4+1}=1$

From the solution presented above, we are able to conclude that the correct answer is C)