Question

Which is the graph of f(x)=1/4(4)×?

Answer 1

`f(x)=(1)/(4)(4)^x\\\\for\ x=1\to f(1)=(1)/(4)\cdot4^1=1\to(1;\ 1)\\\\for\ x=2\to f(2)=(1)/(4)\cdot4^2=(1)/(4)\cdot16=4\to(2;\ 4)`

Answer: The graph nr 4.

Other method:


`f(x)=(1)/(4)\cdot4^x=4^(-1)\cdot4^x=4^(x-1)`

Used:


`a^(-1)=(1)/(a)\\\\a^n\cdot a^m=a^(n\cdot m)`

Draw the graph of y = 4^x and next shift it 1 unit right.

Answer 2

The correct option is D.

Explanation:

Consider the provided function
`f(x)=(1)/(4)(4)^x`

Substitute x = 0 in the above function.

`f(0)=(1)/(4)(4)^0`

`f(0)=(1)/(4)`

Thus, the coordinate is (0,1/4).

Now substitute x = 1.

`f(1)=(1)/(4)(4)`

`f(1)=1`

Thus, the coordinate is(1,1).

Substitute x = 2.

`f(2)=(1)/(4)(4)^2`

`f(2)=(1)/(4)(16)`

`f(2)=4`

Thus, the coordinate is (2,4)

Therefore, the correct option is D.