If f(x) = x3 and g(x) = (x + 1)3, which is the graph of g(x)?
a. a vertical transformation of f(x) 1 unit upward
b. a horizontal transformation of f(x) 1 unit to the left
c. a horizontal transformation of f(x) 1 unit to the right
d. a vertical transformation of f(x) 1 unit downward
e. a vertical transformation of f(x) 3 units downward

The correct option is b.

Step-by-step explanation:

The given function are

From the given function,we get

               .... (1)

The transformation of f(x) is defined as

         ... (2)

Where, a represents the horizontal shift and b represents the vertical shift.

If a>0, the graph of f(x) shifts a units left and if a<0, the graph of f(x) shifts a units right.

If b>0, the graph of f(x) shifts b units upward and if b<0, the graph of f(x) shifts b units downward.

On comparing (1) and (2), we get

Since a=1>0, therefore the graph of g(x) is a horizontal transformation of f(x), 1 unit to the left. Option b is correct.

area = length x width

length = 2 x width

32 = 2 x width x width

32 = 2 x width^2

36 = width ^2  

width = 6

length = 12

area is 32

perimeter = 2 x 12 + 2 x 6 = 24 + 12 = 36

step-by-step explanation: