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

ATranslate each point of the graph of h(x) 3 units up
BTranslate each point of the graph of h(x) 3 units down.
CTranslate each point of the graph of h(x) 3 units right.
DTranslate each point of the graph of h(x) 3 units left.

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Anonymous Anonymous · Answer 1 · 2018-10-10T05:03:59-04:00

We have been given the function \(h(x)=\log_6x\)

Now, we can see that in the transformed function \(h(x)=\log_6(x+3)\), we have added 3 in the x.

Whenever we add/subtract some constant in the x, then the function gets translated to either left or right.

We know that if f(x) is a parent function and if we add a constant c then the function gets shift to c unit left.

Therefore, the given graph will get shifted 3 units left.

D is the correct option.

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

MrRoyal MrRoyal · Answer 2 · 2022-02-14T08:46:07-05:00

To translate h(x) to m(x), you (d) translate each point of the graph of h(x) 3 units left.

The functions are given as:

\(h(x) =log_6(x)\)

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

The rule of translating a function 3 units left is:

\((x,y) \to (x + 3,y)\)

This means that:

h(x) is translated 3 units left to get m

Hence, to get m(x) from m(x), you translate each point of the graph of h(x) 3 units left.