Question

If you are given the graph of h(x)=log6x, how could you graph m(x)=log6(x+3)?

Answer 1

Answer: last option.

Step-by-step explanation:

There are several transformations for a function f(x). Some of them are shown below:

1. If $f(x)+k$, then the function is translated "k" units up.

2. If $f(x)-k$, then the function is translated "k" units down.

3. If $f(x+k)$, then the function is translated "k" units left.

4. If $f(x-k)$, then the function is translated "k" units right.

In this case you have the following function:

$h(x)=log_6x$

And the function m(x) is obtained by transformating the function h(x). This function is:

$m(x)=log_6(x+3)$

Then, based on the transformatios shown before, you can identify that:

$m(x)=h(x+3)$

Therefore, you can determine that you could graph the function  $m(x)=log_6(x+3)$ by translating each point of the graph of the function h(x) 3 units left.