Question

Which of the following shows the graphic representation of the exponential function f(x)=3^x

Answer 1

I believe the answer is B. 

Answer 2

Option B is correct.

Explanation:

The exponential function is in the form of :

`y = ab^x`

where, a is the initial value and b is the growth rate.

If b > 1 , then the graph is exponentially growth.

If 0< b< 1, then the graph is exponentially decay.

Given the exponential function:

`f(x)=y = 3^x`

on comparing with [1] we have;

a =1 and b = 3 > 1

⇒ the function is exponentially growth.

y-intercept:

Substitute x = 0 and solve for y:

then;

`y = 3^0 = 1`

y-intercept = (0, 1)

or

Initial value = 1

End behavior:

If
`x \rightarrow \infty`, then
`f(x) \rightarrow \infty`

and

If
`x \rightarrow -\infty`, then
`f(x) \rightarrow 0`

Therefore, the option B is correct.