Question

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

Answer 1

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

Answer 2

Answer:

Option A is the correct choice.

Step-by-step 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.