Question

Someone help me out please please

Answer 1

We want to check which of the following is true of the graph of the function

`f(x)=((2)/(5))^x`

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

`(-\infty,\infty)`

(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