Question

match each graph below with the appropriate function.
a)
$f(x)=3+\log_{2}x$
$f(x)=-\log_{2}(x+5)$
$f(x)=\log_{2}(x-3)$
$f(x)=-5+\log_{2}x$

Explanation:

Step1: Identify parent function

Parent function: $y=\log_2 x$, vertical asymptote $x=0$, passes through $(1,0)$.

Step2: Analyze graph features

Graph has vertical asymptote $x=0$, shifted downward. At $x=1$, $y=-5$.

Step3: Test candidate functions

For $f(x)=-5+\log_2 x$, substitute $x=1$:
$\log_2 1=0$, so $f(1)=-5+0=-5$, matches the graph.
Check asymptote: $x>0$, same as parent, matches the graph.

Answer:

$\boldsymbol{f(x) = -5 + \log_2 x}$