Question

If you are given the graph of h (x) = log Subscript 6 Baseline x, how could you graph m (x) = log Subscript 6 Baseline (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.

Answer 1

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

Explanation:

Translations

For a > 0

`f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.`

`f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.`

`f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.`

`f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.`

Given functions:

`h(x)= \log_6 x`

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

As m(x) = h(x+3), to graph the function m(x), translate the function h(x) 3 units left.

Answer 2

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

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If the given function is f(x), then rules of translation by b units are:

• Translation up or down by b units is reflected as f(x) + b, or f(x) - b.

• Translation left is given as f(x + b), translation right is given as f(x - b).

Our function and its image are:

• h(x) = log₆ (x) ⇒ m(x) = log₆ (x + 3)

Therefore we have translation left by 3 units.

Correct choice is D.