Answer:
Option A. is the answer.
Step-by-step 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) = [tex]2^{x}-5[/tex]
Now we plug in the values of x to get the values of g(x)
g(-1) = [tex]2^{-1}-5[/tex]
= [tex]\frac{1-10}{2}[/tex]
= [tex]-\frac{9}{2}[/tex] = -4.5
g(0) = [tex]2^{0}-5[/tex]
= 1 - 5 = -4
g(2) = [tex]2^{2}-5[/tex]
= 4 - 5 = -1
g(3) = [tex]2^{3}-5[/tex]
= 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.
