Question

Which point on the graph of g(x)=(1/5)^x? HELPP

Answer 1

Answer:

(-1,5) and $(3, \frac{1}{125})$ are points on the graph

Step-by-step explanation:

Given

$g(x) = \frac{1}{5}^x$

Required

Determine which point in on the graph

To get which of point A to D is on the graph, we have to plug in their values in the given expression using the format; (x,g(x))

A. (-1,5)

x = -1

Substitute -1 for x in $g(x) = \frac{1}{5}^x$

$g(x) = \frac{1}{5}^{-1}$

Convert to index form

$g(x) = 1/(\frac{1}{5})$

Change / to *

$g(x) = 1*(\frac{5}{1})$

$g(x) = 5$

This satisfies (-1,5)

Hence, (-1,5) is on the graph

B. (1,0)

x = 1

Substitute 1 for x

$g(x) = \frac{1}{5}^x$

$g(x) = \frac{1}{5}^1$

$g(x) = \frac{1}{5}$

(1,0) is not on the graph because g(x) is not equal to 0

C. $(3, \frac{1}{125})$

x = 3

Substitute 3 for x

$g(x) = \frac{1}{5}^x$

$g(x) = \frac{1}{5}^3$

Apply law of indices

$g(x) = \frac{1}{5} * \frac{1}{5} * \frac{1}{5}$

$g(x) = \frac{1}{125}$

This satisfies $(3, \frac{1}{125})$

Hence, $(3, \frac{1}{125})$ is on the graph

D.  $(-2, \frac{1}{25})$

x = -2

Substitute -2 for x

$g(x) = \frac{1}{5}^x$

$g(x) = \frac{1}{5}^{-2}$

Convert to index form

$g(x) = 1/(\frac{1}{5}^2)$

$g(x) = 1/(\frac{1}{5}*\frac{1}{5})$

$g(x) = 1/(\frac{1}{25})$

Change / to *

$g(x) = 1*(\frac{25}{1})$

$g(x) = 25$

This does not satisfy  $(-2, \frac{1}{25})$

Hence, $(-2, \frac{1}{25})$ is not on the graph