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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.

User Jon Haddad
by
6.9k points

1 Answer

2 votes

Answer:

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.

User Neurotransmitter
by
6.6k points
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