Question

The logarithmic functions, f(x) and g(x), are shown on the graph.

Answer 1

Answer:

$g(x)=\log (x+1)+4$

Step-by-step explanation:

Translations

For $a > 0$

$f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}$

$f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}$

$f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}$

$f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}$

Parent function:  $f(x)=\log x$

From inspection of the graph, the parent function has been translated 1 unit left and 4 units up.

Function translated 1 unit left:  $f(x+1)=\log (x+1)$

Function translated 4 units up:  $f(x+1)+4=\log (x+1)+4$

Therefore:

$g(x)=\log (x+1)+4$