Question

If f(x) = x3 and g(x) = (x + 1)3, which is the graph of g(x)?

Answer 1

As you can see below, in red is g(x) = (x + 1)^3 and in blue is f(x)=x^3. Adding 1 to x moves the graph to the left by 1.

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Answer 2

the graph of g(x) is a horizontal transformation of f(x) 1 units to the left.

Explanation:

Given the parent function:
`f(x) = x^3`

Rule of Horizontal transformation:

If y =f(x) , then y= f(x+k) gives a function that is translated k units towards the left side.

then;

By definition of horizontal translation:

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

Therefore, the graph of g(x) is a horizontal transformation of f(x) 1 units to the left.