Question

Which is the graph of f(x) = 3 (3/2)^x ?

Answer 1

The answer will be D.

Answer 2

Answer:

The graph of the function f(x) is:

                      Graph  4

Step-by-step explanation:

We are given a function f(x) in terms of variable x as follows:

            $f(x)=3\cdot (\dfrac{2}{3})^x$

Now, when x=0 then the graph of the function f(x) must pass through:

$f(x)=3\cdot (\dfrac{2}{3})^0\\\\i.e.\\\\f(x)=3$

and when x=1 then the graph of the function f(x) must pass through:

$f(x)=3\cdot (\dfrac{2}{3})^1\\\\i.e.\\\\f(x)=2$

i.e. the graph of the function should pass through the points:

(0,3) and (1,2)

Now, after looking at the graph we observe that the first and second graph do  not pass through (0,3).

Hence, graph 1 and graph 2 do not represent the function f(x).

Also, graph 3 pass through (0,3) but it does not pass through (1,2)

Hence, Graph 3 does not represent f(x)

Hence, the correct graph is: Graph 4