Two scientists are running experiments testing the effects of a vaccine on different control groups. the results are shown in the graph using the functions f(x) and g(x): which statement best describes the graph of f(x) and g(x)?
a- the graph of g(x) will eventually exceed the graph of f(x)
b- the graph of f(x) will eventually exceed the graph of g(x)
c- the graphs will both have their y-intercept equal to 5
d- the graphs will both have their y-intercept equal to 2

The correct option is B.

Step-by-step explanation:

The graph of f(x) is g(x) is given.

Graph of both functions intersect each other at a point. Before the point of intersection g(x)>f(x) and after the point of intersection g(x)<f(x).

The graph of f(x) will eventually exceed the graph of g(x). Therefore the correct option is B.

Function g(x)<f(x) for the large value of x, So option A is incorrect.

From the given graph it is clear that the y-intercept of f(x) is 0.2 and y-intercept of g(x) is 2.

So, option C and D are incorrect.

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2

step-by-step explanation:

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