Question

Complete the table of values for the function f(x) = (1/3)x for a, b, and c. x : -2, -1, 0, 1, 2. f(x) : a, b, c, 1/3, 1/9

Answer 1

Given:

The function is

$f(x)=\left(\dfrac{1}{3}\right)^x$

To find:

The missing values for a, b, and c in the given table.

Solution:

We have,

$f(x)=\left(\dfrac{1}{3}\right)^x$

At x=-2,

$f(-2)=\left(\dfrac{1}{3}\right)^{-2}$

$a=\left(3\right)^{2}$         $\left[\because \left(\dfrac{a}{b}\right)^{-n}=\left(\dfrac{b}{a}\right)^{n}\right]$

$a=9$

At x=-1,

$f(-1)=\left(\dfrac{1}{3}\right)^{-1}$

$b=\left(3\right)^{1}$         $\left[\because \left(\dfrac{a}{b}\right)^{-n}=\left(\dfrac{b}{a}\right)^{n}\right]$

$b=3$

At x=0,

$f(0)=\left(\dfrac{1}{3}\right)^{0}$

$c=1$         $\left[\because a^0=1, a\neq 0\right]$

Therefore, the missing values of a,b and c are 9, 3, and 1 respectively.

Answer 2

Answer: below

Step-by-step explanation: