Question

Graph the exponential function
g(x)=(2/5)^x
Plot five points on the graph of the function.

Answer 1

To graph the function g(x)=(2/5)^x, we can choose a few values of x and calculate the corresponding values of g(x).

Let's choose x=-2, -1, 0, 1, and 2:

For x=-2:
g(-2) = (2/5)^-2 = (5/2)^2 = 25/4 = 6.25

For x=-1:
g(-1) = (2/5)^-1 = 5/2 = 2.5

For x=0:
g(0) = (2/5)^0 = 1

For x=1:
g(1) = (2/5)^1 = 2/5 = 0.4

For x=2:
g(2) = (2/5)^2 = 4/25 = 0.16

Now, we can plot these points on the graph:

(-2, 6.25)
(-1, 2.5)
(0, 1)
(1, 0.4)
(2, 0.16)

The graph of the function g(x)=(2/5)^x is as follows:

{{{ graph( 500, 500, -5, 5, -1, 7, (2/5)^x) }}}