The graph of is given by,
Here given the function is
when , then it passes through the origin (0,0).
When
Since we know that, , then the function has maximum height at
.
Again when , again the function is 0.
So clearly the function is the Oscillating function.
Using graphing calculator we get the graph of function ,
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The function which has range (2, infinity) from the provided function is y = 5ˣ +2. Option 4 is correct.
<h3>What is range of function?</h3>Range of a function is the set of all the possible output values which are valid for that function.
The function whose range is (2, ∞) has to be find out.
The first function given in the problem is,
This function has the periodic function with period of logarithmic function and the range of this function is all the real number. This is not the correct option.
The second function given in the problem is,
This function has the periodic function with period of logarithmic function and the range of this function is all the real number. This is not the correct option.
The fourth function given in the problem is,
This function is translated 5 units up to the function 5ˣ which has the range (0,∞).
Thus, the range of this function is (2, ∞).
Hence, the function which has range (2, infinity) from the provided function is y = 5ˣ +2. Option 4 is correct.
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We have been given the expression
We have the exponent rule
Using this rule, we have
Now, using the fact that , we get
D is the correct option.
