Question

Complete the table for the following function y=(1/3)^x

Answer 1

x=-3 then y= 27

x= -2 then y= 9

x=2 then y: $y=\frac{1}{9}$

x=3 then y: $y=\frac{1}{27}$

The graph of the function decreases from left to right.

Option C is correct.

Step-by-step explanation:

We are given the function: $y=(\frac{1}{3})^x$

and we need to fill the table

if x = -3 then y=?

Putting value of x in the given function:

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

$y=(\frac{1}{3})^-3$

Applying exponent rule a^-b= 1/a^b

$y=\frac{1}{(\frac{1}{3})^3 }\\y=\frac{1}{\frac{1}{27}}\\y=27$

if x = -2 then y=?

Putting value of x in the given function:

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

$y=(\frac{1}{3})^-2$

Applying exponent rule a^-b= 1/a^b

$y=\frac{1}{(\frac{1}{3})^2 }\\y=\frac{1}{\frac{1}{9}}\\y=9$

if x = 2 then y=?

Putting value of x in the given function:

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

$y=(\frac{1}{3})^2$

Applying exponent rule a^-b= 1/a^b

$y=\frac{1}{(\frac{1}{3})^2 }\\y=\frac{1}{9}$

if x = 3 then y=?

Putting value of x in the given function:

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

$y=(\frac{1}{3})^3$

Applying exponent rule a^-b= 1/a^b

$y=\frac{1}{(\frac{1}{3})^3 }\\y=\frac{1}{27}$

So, x=-3 then y= 27

x= -2 then y= 9

x=2 then y: $y=\frac{1}{9}$

x=3 then y: $y=\frac{1}{27}$

Graph of the function is shown in figure attached.

The graph of the function decreases from left to right.

Option C is correct.

Keywords: Solving Equations

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