Question

What function is represented below?

Answer 1

Answer:

The correct option is 3, i.e., $f(x)=(\frac{1}{4})^{x-2}$.

Step-by-step explanation:

From the graph it is clear that as x tends to infinity, then the value of function tends to 0 and y-intercept of the function is at above (0,8).

In option 1:

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

At x=0,

$f(0)=(\frac{1}{4})^{0+2}=0.063$

The y-intercept of this function is 0.063, which is less than 8, therefore option 1 is incorrect.

In option 2:

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

At x=0,

$f(0)=(\frac{1}{4})^{0}+2=3$

The y-intercept of this function is 3, which is less than 8, therefore option 2 is incorrect.

In option 3:

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

At x=0,

$f(0)=(\frac{1}{4})^{0-2}=16$

The y-intercept of this function is 16, which is more than 8, therefore option 3 is correct.

In option 4:

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

At x=0,

$f(0)=(\frac{1}{4})^{0}-2=-1$

The y-intercept of this function is -1, which is less than 8, therefore option 4 is incorrect.

Answer 2

By graphing the given options as shown in attached figure
f(x) = (1/4)^x+2   ⇒⇒⇒⇒ The black graph
f(x) = (1/4)^x +2  ⇒⇒⇒⇒ The red graph
f(x) = (1/4)^x-2    ⇒⇒⇒⇒ The blue graph
f(x) = (1/4)^x -2   ⇒⇒⇒⇒ The green graph


The correct answer will be the blue graph

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