Question

If you are given the graph of h(x) = log6X, how could you graph m(x) =log6(X+3)?

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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.

Answer 1

Translate each point of the graph of h(x) 3 units left ⇒ 4th answer

Explanation:

Let us revise the translation of a graph

• If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)
• If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)
• If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k
• If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - k

∵
`h(x)=log_(6)(x)`

∵
`m(x)=log_(6)(x+3)`

∵ x in h(x) is changed to (x + 3) in m(x)

- From the 2nd rule above, that means the graph of h(x)

is translated 3 units to the left

∴ The graph of h(x) is translated 3 units to the left

∴ Each point on the graph of h(x) is translated 3 units to the left

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

Look to the attached figure to more understand

The red line represents h(x)

The blue line represents m(x)