Question

Graph the equation F(x)=(1/3)^x

Answer 1

The value of a=9,b=3 and c=1

Explanation:

The graph shown is for function f(x)

The given function is f(x)=
`((1)/(3)) ^(x)`

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)=
`((1)/(3)) ^(x)`

f(-2)=
`((1)/(3)) ^((-2))`

a=
`((1)/(3^((-2))))`

a=
`3^((2))`

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)=
`((1)/(3)) ^(x)`

f(-1)=
`((1)/(3)) ^((-1))`

b=
`((1)/(3^((-1))))`

b=
`3^((1))`

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)=
`((1)/(3)) ^(x)`

f(0)=
`((1)/(3)) ^((0))`

c=
`((1)/(3^((0))))`

c=1