Question

What is the range of the exponential function shown below

Answer 1

Answer:

The correct option is C.

Step-by-step explanation:

Range is the set of output or the values of the function.

The given function is

$f(x)=9\cdot 2^x$

If a exponential function is defined as g(x)=a^x, where a>0, then the value of g(x) is always greater than 0, g(x)>0.

It means,

$2^x>0$

Multiply both sides by 9.

$9\cdot 2^x>9\cdot 0$

$9\cdot 2^x>0$

$f(x)>0$

The value of the function f(x) is always greater than 0, therefore the range of the function is

Range = { y | y>0}

Hence the correct option is C.

Answer 2

Answer : y>0

f(x) = 9*2^x

f(x) is an exponential function

$f(x) = 9*2^x$

When we plug in positive value for x , the value of y is positive

When we plug in negative value for x , the value y is also positive

So for any value of x, the y value is positive always.

Range is the set of y values for which the function is defined

y values are positive , so range is y >0