Question

Suppose that g(x) = f(x-2) + 7. Which statement best compares the graph of

g(x) with the graph of f(x)?
O
A. The graph of g(x) is the graph of f(x) shifted 2 units to the right
and 7 units up.
O
B. The graph of g(x) is the graph of f(x) shifted 2 units to the left and
7 units up.
O
C. The graph of g(x) is the graph of f(x) shifted 2 units to the right
and 7 units down.
O
D. The graph of g(x) is the graph of f(x) shifted 2 units to the left and
7 units down.

Answer 1

Option A) is correct.

Explanation:

The given equation is as,
`g(x) = f(x-2) + 7`.

Lets focus on graph f(x-2).

Take any example, like
`y = x`. It passes through origin.

Now replace x by (x-2). Now
`y = x-2`, it passes through x=2, thus shifted to right by 2 units.

Now consider the function g(x). If the constant 7 was not there, value would be f(x-2). But adding a positive constant (+ 7) moves the graph up by 7 units.

Thus overall, The graph of g(x) is the graph of f(x) shifted 2 units to the right and 7 units up.