Question

If you are given the graph of h(x) = log. x, how could you graph m(x) = log2(x+3)?

O Translate each point of the graph of h(x) 3 units up.
O Translate each point of the graph of h(x) 3 units down.
O Translate each point of the graph of h(x) 3 units right.
O Translate each point of the graph of h(x) 3 units left.

Answer 1

Option (d).

Explanation:

Note: The base of log is missing in h(x).

Consider the given functions are

`h(x)=\log_2x`

`m(x)=\log_2(x+3)`

The function m(x) can be written as

`m(x)=h(x+3)` ...(1)

The translation is defined as

`m(x)=h(x+a)+b` .... (2)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

On comparing (1) and (2), we get

`a=3,b=0`

Therefore, we have to translate each point of the graph of h(x) 3 units left to get the graph of m(x).

Hence, option (d) is correct.