SOLUTION
We want to check which of the following is true of the graph of the function
[tex]f(x)=(\frac{2}{5})^x[/tex]The graph of the function is shown below
(A) the y-intercept is (0, 1). This is true, you can see that the graph cuts the y-axis at (0, 1)
(B) It is increasing. This is false. There is no point where the graph is increase, rather it is decreasing (slopes downwards) up to x = 2.5, then remains constant.
(C) The x-intercept is (1, 0). This is false. It doesn't cut the x-axis at (1, 0)
(D) The domain of f(x) is x > 0. This is false. The domain is valid for all real numbers, both positive and negative.
Hence the domain is
[tex](-\infty,\infty)[/tex](E). It is decreasing. This is true, we can see that the graph slopes downwards and remain constant.
(F) The range of F(x) is y > 0. This is true, we can see that the y-values starts from zero and then move up to positive numbers
