Question

Which of these statements is true for f(x)=3•(9)^x

Answer 1

A. The y-intercept is (0,3)

Answer 2

Option A is the correct choice.

Explanation:

We have been given an equation
`f(x)=3\cdot (9)^x`. We are asked to choose the correct statement about our given equation.

Let us see our given choices one by one.

A. The y-intercept is (0,3).

Let us find the y-intercept by substituting
`x=0` in our given equation.

`f(0)=3\cdot (9)^0`

`f(0)=3\cdot 1`

`f(0)=3`

Since the y-intercept of our given equation is (0,3), therefore, option A is the correct choice.

B. It is always decreasing.

We can see from our given equation that our given function represents exponential growth, where growth factor is 9, therefore, option B is not correct.

C. The domain of
`f(x)` is
`x>0`.

Since our function is defined for all real values of x, therefore, the domain of function is
`(-\infty,\infty)` and our given statement is not true.

D. The y-intercept is (0,1).

Since the y-intercept of our given equation is (0,3), therefore, option D is not a correct choice.