Part 1) The first four terms of a sequence are shown below.
Let
[tex] f(1)=8\\ f(2)=5\\ f(3)=2\\ f(4)=-1 [/tex]
we know that
[tex] f(2)-f(1)=5-8\\ f(2)-f(1)=-3\\ f(2)=f(1)-3 [/tex]
[tex] f(3)-f(2)=2-5\\ f(3)-f(2)=-3\\ f(3)=f(2)-3 [/tex]
[tex] f(4)-f(3)=-1-2\\ f(4)-f(3)=-3\\ f(4)=f(3)-3 [/tex]
So
[tex] f(n+1)=f(n)-3 [/tex]
therefore
the answer part 1) is the option
[tex] f(1) = 8, f(n + 1) = f(n) - 3; for. n\geq 1 [/tex]
Part 2) Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x) + 20?
Let
(a,b)--------->represent a point in the graph of f(x)
we know that
In the new function f(x)+d
(a,b)-----------> become-------> (a,b+d)
So
The new function f(x)+d shift up by d
therefore
in the new function [tex] f(x)+20 [/tex]-------> the graph of f(x) shift up by [tex] 20 [/tex]
the answer part 2) is the option
The graph of y = f(x) will shift up [tex] 20 [/tex] units.
Part 3) Every week Annie plants 2 saplings in her garden. The function below shows the total number of saplings f(w) in her garden after w weeks.
[tex] f(w) = 2w + 3 [/tex]
we know that
The y-intercept is when the value of w is equal to zero
the value of f(w) for
[tex] w=0 [/tex]
represent the original number of saplings in Annie's garden
so
For
[tex] w=0\\ f(0)=2*0+3\\ f(0)=3 [/tex]
therefore
the answer is the option
It is equal to [tex] 3 [/tex] and represents the original number of saplings in Annie's garden.
