Question

Compare the graphs below of the logarithmic functions. Write the equation to represent g(x).

Answer 1

Answer:

g(x) = log(x) + 4

Step-by-step explanation:

The graph of $g(x)$ is the graph of $f(x)$ shifted along the positive y-direction by 4 units. We know this because $f(x)$ goes flat as it approaches $y =1,$ and $g(x)$ goes flat when $y = 5$; therefore, the function $g(x)$ is a shifted version of $f(x)$, and it is

$g(x) = f(x)+4$

$\boxed{g(x) = log(x)+4}$

We can confirm this by putting $x =1$ into the function, and we get:

$f(1) = log(1) = 0$,

and the graph of $f(x)$ confirms this.

$g(1) = log(1)+4 = 4$,

which the graph of  $g(x)$ confirms.