Answer
$y=\log_2{x}$
Work Step by Step
The graph contains the point $(\frac{1}{2}, -1)$.
This means that the x and y-coordinates of this point satisfy the equation $y=\log_a{x}$.
Substitute the x and y values into the given equation to obtain:
$-1 = \log_a{(\frac{1}{2})}$
RECALL:
$y=\log_a{x} \longrightarrow a^y=x$
Use the rule above to obtain:
$-1 = \log_a{(\frac{1}{2})} \longrightarrow a^{-1} = \frac{1}{2}$
Note that $\frac{1}{2} = 2^{-1}$. So the expression above is equivalent to:
$a^{-1} = 2^{-1}$
Use the rule $a^x = b^x \longrightarrow a = b$ to obtain:
$a=2$
Thus, the equation of the function whose graph is given is $y=\log_2{x}$.
