Question

Which function is graphed below?
y=j3)

Answer 1

`y = 3((1)/(3) )^(x)`

Explanation:

See the attached graph.

The points (0,3) and (1,1) are on the graph of the exponential function.

Let the function be
`y = a(b)^(x)` ....... (1)

Now, satisfying the point (0,3) we get from the equation (1),

`3 = a(b)^(0) = a`

Therefore, the initial value of the function is a = 3

Hence, the equation becomes
`y = 3(b)^(x)` ......... (2)

Now, satisfying the point (1,1) we get from equation (2)

`1 = 3 (b)^(1)`

⇒ b = 1/3

So, the final equation becomes
`y = 3((1)/(3) )^(x)` (Answer)