Question

Which is the graph of f (x) = 4 (1/2) Superscript x?

Answer 1

Answer:

Option (2) is correct graph.

Step-by-step explanation:

Given:

The function to graph is given as:

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

Now, the above function is an exponential function of the form $f(x)=ka^x$

Where, 'k' and 'a' are constants.

The range of an exponential function is always greater than 0.

The domain is all real numbers.

Now, for graphing it, we need to find some points on it and its end behaviour.

Now, for x = 0, the function value is given as:

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

So, (0, 4) is a point on the graph.

Now, for x = 1, the function value is given as:

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

So, (1, 2) is another point on the graph.

Now, for x = 2, the function value is given as:

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

So, (2, 1) is another point on the graph.

Now, as 'x' tends to ∞, the function value tends to:

$f(x\to\infty)=4\cdot\frac{1}{2}^{\infty}=\frac{4}{\infty}=0$

So, as

$x\to\infty,f(x)\to0\\\\x\to-\infty,f(x)\to\infty$

Now, from among all the options, only option (2) fulfills all the conditions given above.

So, option (2) is correct graph.