Question

Which transformation of f(x) will produce the same graph as g(x)?

a) H(x) = f(x+1)
b) H(x) = f(x) + 1
c) H(x) = 2x
d) H(x) = f(x-1)

Answer 1

The correct transformation of f(x) that will produce the same graph as g(x) is H(x) = f(x-1).

Step-by-step explanation:

The correct transformation of f(x) that will produce the same graph as g(x) is option d) H(x) = f(x-1).

This transformation involves translating the graph of f(x) in the positive x-direction by a distance of 1 unit. This means that every point on the graph of f(x) will be shifted 1 unit to the right, resulting in the same graph as g(x).

For example, if the point (2, 3) lies on the graph of f(x), after applying the transformation H(x) = f(x-1), the point will be shifted to (1, 3) which will lie on the graph of g(x).