The value of a=9,b=3 and c=1
Step-by-step explanation:
The graph shown is for function f(x)
The given function is f(x)=[tex](\frac{1}{3}) ^{x}[/tex]
Table says,
X Y
-2 a
1 b
0 c
1 (1/3)
2 (1/9)
To find value of a:
From table, for output value a, input value, x=(-2)
we can write f(-2)=a
Therefore,
f(x)=[tex](\frac{1}{3}) ^{x}[/tex]
f(-2)=[tex](\frac{1}{3}) ^{(-2)}[/tex]
a=[tex](\frac{1}{3^{(-2)}})[/tex]
a=[tex]3^{(2)}[/tex]
a=9
To find value of b:
From table, for output value a, input value, x=(-1)
we can write f(-1)=b
Therefore,
f(x)=[tex](\frac{1}{3}) ^{x}[/tex]
f(-1)=[tex](\frac{1}{3}) ^{(-1)}[/tex]
b=[tex](\frac{1}{3^{(-1)}})[/tex]
b=[tex]3^{(1)}[/tex]
b=3
To find value of c:
From table, for output value a, input value, x=(0)
we can write f(0)=c
Therefore,
f(x)=[tex](\frac{1}{3}) ^{x}[/tex]
f(0)=[tex](\frac{1}{3}) ^{(0)}[/tex]
c=[tex](\frac{1}{3^{(0)}})[/tex]
c=1
