Question

Select the correct answer. Consider the function (x) = 3 and the function g, which is shown below. (1) – 2 = 3" – 2 . How will the graph of g differ from the graph of 1? O A. The graph of gis the graph of fshifted 2 units up. OB. The graph of g is the graph of fshifted 2 units down. O C. The graph of g is the graph of fshifted 2 units to the right. OD The graph of g is the graph of fshifted 2 units to the left.

Answer 1

Given:

`f(x)=3^x`
`g(x)=f(x)-2=3^x-2\ldots\ldots(1)`

If a function f(x) is shifted h units vertically, then the new function is given as,

`g(x)=f(x)+k\ldots\ldots.(2)`

If k is positive, the graph of f(x) will shift up and if k is negative, f(x) will shift down by k units.

Comparing (2) with (1), we find that k=-2.

So, the graph f(x) gets shifted -2 units down.

Hence, the graph of g is the graph of f shifted 2 units down.

Option (B) is correct.