Question

Please Help ASAP
Select the true statement regarding the end behavior of the functions.

Answer 1

Option A. is the answer.

Explanation:

In the given table for f(x), we see that for every value of x, function f(x) is decreasing.

f(-2) = 48

f(0) = 12

f(2) = 3

f(3) = 1.5

In other words as the value of x increases, f(x) is approaching towards 0.

Now we take another function g(x) =
`2^(x)-5`

Now we plug in the values of x to get the values of g(x)

g(-1) =
`2^(-1)-5`

=
`(1-10)/(2)`

=
`-(9)/(2)` = -4.5

g(0) =
`2^(0)-5`

= 1 - 5 = -4

g(2) =
`2^(2)-5`

= 4 - 5 = -1

g(3) =
`2^(3)-5`

= 8 - 5

= 3

Now we find that g(x) is increasing with the values of x.

Now we take third function h(x). By analyzing the given graph we find

h(-4) = 2

h(0) = 3

h(1) = 5

So when we are increasing the value of x function h(x) is increasing.

Finally we conclude by the options given that f(x) is the only function which tends to 0 with the increase in the values of x.

Option A. is the answer.