Question

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

Answer 1

B. a horizontal transformation of f(x) 1 unit to the left

Answer 2

The correct option is b.

Explanation:

The given function are

`f(x)=x^3`

`g(x)=(x+1)^3`

From the given function,we get

`g(x)=f(x+1)` .... (1)

The transformation of f(x) is defined as

`g(x)=f(x+a)+b` ... (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

`a=1,b=0`

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.