Question

The graph of g(x) is the result of translating the graph of f(x)=3x six units to the right. what is the equation of g(x)?

Answer 1

Translation of a f(x) by h units (to the right) is given by g(x)=f(x-h)

For the case where f(x)=3x, then
g(x)=f(x-3)=3(x-3)=3x-9

Answer 2

g(x) = 3(x-3)

Explanation:

The parent function is given by
`f(x)=3x`

The function g(x) is obtained by translating the graph of f(x) by 6 units right.

We know that if f(x) is translated 'a' units right then the resultant function be f(x-a).

Here, f(x) is translated right by 6 units. Thus, we have

a = 6

And the function g(x) would be

g(x) = f(x-3)

g(x) = 3(x-3)

Thus, the equation of g(x) is g(x) = 3(x-3)