Question

Which facts are true for the graph of the function below? Check all that apply.

F(x)=(3/7)^x
A. The x-intercept is (1, 0).
B. It is decreasing.
C. It is increasing.
D. The y-intercept is (0, 1).
E. The domain of F(x) is x > 0.
F. The range of F(x) is y > 0.

Answer 1

the answers are b,d, and f. I got it correct.

Answer 2

B. It is decreasing function

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

F.The range of F(x) is y > 0

Explanation:

We are given that a function

`f(x)=((3)/(7))^x`

We have to find the facts which are true about the graph of the given function.

Substitute x=0 then, we get

`f(x)=((3)/(7))^0=1` because (
`a^0=1`)

Therefore, y- intercept is (0,1).

It is defined for all real number .Therefore, domain of given function is all real numbers .

Domain of F(x)=R

Range of F(x):y >0

`lim_{x\rightarrow\infty)((3)/(7))^x=0`

`\lim_(x\rightarrow-\infty)((3)/(7))^x=\infty`

Hence, it is decreasing function.

Answer:B. It is decreasing function

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

F.The range of F(x) is y > 0