If you are given the graph of h(x)=log6x. how could you graph m(x)=log6(x+3)
A. Translate each point of the graph of h(x) 3 units up
B. Translate each point of the graph of h(x) 3 units down.
C. Translate each point of the graph of h(x) 3 units right.
D. Translate each point of the graph of h(x) 3 units left.

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Аноним Аноним · Answer 1 · 2018-10-10T11:03:59+02:00

We have been given the function [tex]h(x)=\log_6x[/tex]

Now, we can see that in the transformed function [tex]h(x)=\log_6(x+3)[/tex], 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 · 2022-02-14T14:46:07+01:00

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:

[tex]h(x) =log_6(x)[/tex]

[tex]m(x) =log_6(x + 3)[/tex]

The rule of translating a function 3 units left is:

[tex](x,y) \to (x + 3,y)[/tex]

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.