Question

which is the graph of f(x)=1/4(4)×?

Answer 1

$f(x)=\dfrac{1}{4}(4)^x\\\\for\ x=1\to f(1)=\dfrac{1}{4}\cdot4^1=1\to(1;\ 1)\\\\for\ x=2\to f(2)=\dfrac{1}{4}\cdot4^2=\dfrac{1}{4}\cdot16=4\to(2;\ 4)$

Answer: The graph nr 4.

Other method:

$f(x)=\dfrac{1}{4}\cdot4^x=4^{-1}\cdot4^x=4^{x-1}$

Used:

$a^{-1}=\dfrac{1}{a}\\\\a^n\cdot a^m=a^{n\cdot m}$

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

Answer 2

Answer:

The correct option is D.

Step-by-step explanation:

Consider the provided function $f(x)=\frac{1}{4}(4)^x$

Substitute x = 0 in the above function.

$f(0)=\frac{1}{4}(4)^0$

$f(0)=\frac{1}{4}$

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

Now substitute x = 1.

$f(1)=\frac{1}{4}(4)$

$f(1)=1$

Thus, the coordinate is(1,1).

Substitute x = 2.

$f(2)=\frac{1}{4}(4)^2$

$f(2)=\frac{1}{4}(16)$

$f(2)=4$

Thus, the coordinate is (2,4)

Therefore, the correct option is D.