The graph of f(x) = 10(1/2)^x is graphed. What is the range of the function?  

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crmhaske's profile pic

crmhaske | College Teacher | (Level 3) Associate Educator

Posted on

The graph of the function `f(x)=10(1/2)^x` is:

The range of the function is defined as all possible values of y.  From the graph we can see that the range of y is y>0.

We can also tell from the function itself.  As both 10 and 0.5 are positive numbers the function will never be equal to less than 0, and no value of x will make y=0.

Sources:
pramodpandey's profile pic

pramodpandey | College Teacher | (Level 3) Valedictorian

Posted on

We have given

`y=10(1/2)^x`

since `(1/2)^x>0`  for all values of x. Thus `y>0 AAx`

Thus range of y={x :`x in(0,oo)` ,x is real number}

`y!=0` for any value of x.

The Graph of the y is shown above.Red line shows when `x<=0`  and green line shows when `x>=0`

When x=0  then y=10.

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