Answer : y>0
f(x) = 9*2^x
f(x) is an exponential function
[tex]f(x) = 9*2^x[/tex]
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
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
[tex]f(x)=9\cdot 2^x[/tex]
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,
[tex]2^x>0[/tex]
Multiply both sides by 9.
[tex]9\cdot 2^x>9\cdot 0[/tex]
[tex]9\cdot 2^x>0[/tex]
[tex]f(x)>0[/tex]
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.
