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

Translate each point of the graph of h(x) 3 units up.
Translate each point of the graph of h(x) 3 units down.
Translate each point of the graph of h(x) 3 units right.
Translate each point of the graph of h(x) 3 units left.

1 Answer

5 votes

Answer: last option.

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.

User Augustine Jose
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