Question

Help me out please please

Answer 1

`\begin{gathered} f(x)=((2)/(5))^{x\text{ }} \\ \\ For\text{ y-intercept, x=0}.So: \\ f(0)=((2)/(5))^0 \\ f(0)^=1 \\ Intercept(0,1) \end{gathered}`

THE CORRECT OPTIONS ARE: A, E and F

First one is correct

Let's see if it is increasing.

`\begin{gathered} ifx=\text{ -1} \\ f(\text{ -}1)=((2)/(5))^{\text{ -1}} \\ f(\text{ -1\rparen = }(1)/((2)/(5)) \\ f(\text{ -1\rparen= }(5)/(2)\text{ = 2.5} \\ \\ ifx=2 \\ f(2)=((2)/(5))^2 \\ f(2)=(2^2)/(5^2) \\ f(2)=(4)/(25)=0.16 \end{gathered}`

So, it is decreasing. B is incorrect.

3) The x-intercept is 0.

To find the x-intercept we need to make f(x)=0

`\begin{gathered} 0=((2)/(5))^x \\ x=\infty \end{gathered}`

There is no X number which makes the equation 0. It has no X intercept. C is incorrect

D) the domain is x>0. Wrong. I made x = -1 in the example above, and it exists. So it is incorrect.

E) It is decreasing. Correct

F)The range is y>0. Correct. For any number in an exponential function, the range is always going to be a positive number different than 0, because range (0, infinite)