Complete the table of values for the function:
[tex]
\begin{array}{l}
f(x)=\left(\frac{1}{3}\right)^x \\
a=9 \\
b=3 \\
c=1
\end{array}
[/tex]
When [tex]$b\ \textgreater \ 1$[/tex], as [tex]$x$[/tex] grows in the negative direction, [tex]$y \square$[/tex]. When [tex]$0\ \textless \ b\ \textless \ 1$[/tex], as [tex]$x$[/tex] grows in the negative direction, [tex]$y \square$[/tex].
| x | f(x) |
| --- | ---- |
| -2 | a |
| -1 | b |
| 0 | c |
| 1 | 1/3 |
| 2 | 1/9 |
Answer (2)
Calculate f ( − 2 ) = ( 3 1 ) − 2 = 9 , so a = 9 .
Calculate f ( − 1 ) = ( 3 1 ) − 1 = 3 , so b = 3 .
Calculate f ( 0 ) = ( 3 1 ) 0 = 1 , so c = 1 .
Since 0 < b < 1 , as x grows in the negative direction, y grows. The completed table is:
x
f(x)
-2
9
-1
3
0
1
1
1/3
2
1/9
When $0
To complete the table for f ( x ) = ( 3 1 ) x , we calculated values and found that a = 9 , b = 3 , and c = 1 . The completed table is provided, along with an explanation of how the function behaves based on the values of b . Overall, as x decreases, y increases for this specific case.
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