Respuesta :
[tex]\begin{gathered} f(x)=(\frac{2}{5})^{x\text{ }} \\ \\ For\text{ y-intercept, x=0}.So: \\ f(0)=(\frac{2}{5})^0 \\ f(0)^=1 \\ Intercept(0,1) \end{gathered}[/tex]
THE CORRECT OPTIONS ARE: A, E and F
First one is correct
Let's see if it is increasing.
[tex]\begin{gathered} ifx=\text{ -1} \\ f(\text{ -}1)=(\frac{2}{5})^{\text{ -1}} \\ f(\text{ -1\rparen = }\frac{1}{\frac{2}{5}} \\ f(\text{ -1\rparen= }\frac{5}{2}\text{ = 2.5} \\ \\ ifx=2 \\ f(2)=(\frac{2}{5})^2 \\ f(2)=\frac{2^2}{5^2} \\ f(2)=\frac{4}{25}=0.16 \end{gathered}[/tex]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
[tex]\begin{gathered} 0=(\frac{2}{5})^x \\ x=\infty \end{gathered}[/tex]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)
