Answer :
The function shown in the graph is y = log₆ (x)
How do we know the function shown in the graph?
By examining each alternative and substituting the given x coordinates into the provided choices, we can evaluate their corresponding y values.
Upon plugging x = 6 into choice A, we obtain y = -1, which does not align with our desired y = 1. Therefore, choice A can be eliminated from consideration.
Applying x = 6 to choice B yields y = -2.6 approximately, which does not meet the required criteria. Hence, this option is also unsuitable.
Next, we attempt x = 6 in choice C, only to encounter a division by zero error. Consequently, choice C can be disregarded.
The sole remaining option is choice D. This function proves valid as x = 0.5 yields y = -0.4 approximately. Moreover, the input-output pairs of x = 1 and y = 0, as well as x = 6 and y = 1, align correctly.
Please note that the computation of logarithmic values may necessitate the use of the change of base formula, which states that log(b,x) = log(x)/log(b).
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