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Dylan looked at the function[tex]f(x) = 4( \frac{1}{2} )^{x} [/tex]and said, "This function is always greater than 0, so 0 is the absolute minimum." Explain why Dylan is incorrect.

Answer :

The function is

[tex]f(x)=4(\frac{1}{2})^x[/tex]

The given function is an exponential function.

A characteristic of these type of function is that it never crosses the x-axis.

If the base is between 0 and 1 and positive, then the function will be always over the x-axis.

The greater the value of x, the more close it would come to the x-axis but it will never reach it, this is called an horizontal asympote.→ since it has an horizontal asympote it will never be zero, it means that it does not have a minimum value, it just keeps decreasing until infinity.

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