Alena is a farmer. T ( A ) T(A)T, left parenthesis, A, right parenthesis models the time (in minutes) it takes Alena to plow an area of A AA square meters. A AA 100 100100 120 120120 180 180180 T ( A ) T(A)T, left parenthesis, A, right parenthesis 470 470470 564 564564 846 846846 When does the plowing time increase faster? Choose 1 Choose 1 (Choice A) A Between an area of 100 100100 square meters and an area of 120 120120 square meters (Choice B) B Between an area of 120 120120 square meters and an area of 180 180180 square meters (Choice C) C The plowing time increases at the same rate over both intervals

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step-by-step explanation:

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let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

step-by-step explanation: