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

Answer:

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

----------------------------

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.

Answer 2

Answer:

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

Step-by-step 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.