Questions: a. f(x)=-log4(x) b. f(x)=log(1/6)(x) c. f(x)=log4(x) d. f(x)=-log(1/6)(x)

a. f(x)=-log4(x) b. f(x)=log(1/6)(x) c. f(x)=log4(x) d. f(x)=-log(1/6)(x)
Transcript text: a. $f(x)=-\log _{4}(x)$ b. $f(x)=\log _{\frac{1}{6}}(x)$ c. $f(x)=\log _{4}(x)$ d. $f(x)=-\log _{\frac{1}{6}}(x)$
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Solution

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Solution Steps

Step 1: Analyze the graph

The graph is of a logarithmic function. It passes through the point (1,0) and is decreasing. This tells us the base of the logarithm is greater than 1. The graph is not reflected over the x-axis.

Step 2: Evaluate the options

Option c, _f(x) = log4(x)_ makes sense since when _x_ = 1, _f_(1) = log4(1) = 0 and when _x_ = 4, _f_(4) = log4(4) = 1 which approximately match the graph.

Option a can be eliminated as the negative sign reflects the graph over the x-axis, which doesn't match the given graph. Options b and d can also be eliminated since the bases are less than one which suggests the graph should be increasing.

Final Answer: The equation of the graph is c. _f(x) = log4(x)_

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