Since an arithmetic sequence is a sequence of numbers and the difference of any two successive members of the sequence is a constant
So this question is arithmetic because it keep minus by 7
from 19 - 7 = 12
12 - 7 = 5
5 - 7 = -2
so common difference is -7
or you can check with arithmetic formular as
=
+ (n−1)d
I will just put in the 4th term which is -2 and n will equal to 4
and is the 1st term which is 19
-2 = 19 + (4−1)d
-2 - 19 = 3d
d =
d = -7
We have been given a graph of function g(x) which is a transformation of the function
Now we have to find the equation of g(x)
Usually transformation involves shifting or stretching so we can use the graph to identify the transformation.
First you should check the graph of
You will notice that it is always above x-axis (equation is x=0). Because x-axis acts as horizontal asymptote.
Now the given graph has asymptote at x=-2
which is just 2 unit down from the original asymptote x=0
so that means we need shift f(x), 2 unit down hence we get:
but that will disturb the y-intercept (0,1)
if we multiply by 3 again then the y-intercept will remain (0,1)
Hence final equation for g(x) will be:
