Question

1. Is down below and is the first photo.

2. The graph shows f(x) and its transformation g(x).
Enter the equation for g(x) in the box.
g(x)=

3. What ia the domain and range of the relation shown in the table?
X -12, -8, 0, 1
Y 0, 12, 0, 8

Answer 1

1.
`a_(n)=(1)/(3) a_(n-1)` where
`a_(1) =27`

2.
`2^(x+1)`

3. The domain is {-12,-8,0,1}. The range is {0,12,8}.

Explanation:

1. The recursive formula is defined as an implicit way of writing the rule of a function or pattern. It is implicit because it uses previous terms to find the next term in the pattern. We multiply, add, subtract or divide a previous term by a constant value or expression to find the next. In this case, 27 becomes 9 through division by 3 or multiplication by 1/3. The pattern continues 9(1/3)=3 and so forth.

2. The function f(x) is an exponential and has a general form of
`y=ab^x`. We know f(x) is
`2^x`. The points of g(x) all changed from f(x) by shifting over to the left. This transformation occurred by
`2^(x+1)`.

3. Domain is defined as the set of all x-values. Range is defined as the set of all y-values. The domain is {-12,-8,0,1}. The range is {0,12,8}.