Answer:
The second choice.
Step-by-step explanation:
The log(x) ----> log(2x) compresses the graph horizontally by a factor of 2 .
The + 3 translates up 3.
The second choice is the correct one.
Answer:
Option 2 - It is compressed horizontally by a factor of 2 and translated up 3.
Step-by-step explanation:
Given : The graph [tex]y=\log(2x)+3[/tex] and [tex]y=\log(x)[/tex]
To find : How does the graph of [tex]y=\log(2x)+3[/tex] related to the graph of [tex]y=\log(x)[/tex]
Solution :
The parent function be [tex]y=\log(x)[/tex]
Horizontally Compressed:
If y =f(x) , then y =f(bx) gives a horizontal compression if b>1.
Multiplying the parent function by 2 means you are compressing it horizontally,
i,e [tex]y=\log(x) \rightarrow \text{Horizontally compressed by 2} \rightarrow y=\log(2x)[/tex]
Translated up :
i.e, f(x)→f(x)+b
Adding 3 means you are moving it up by 3 units
[tex]y=\log(2x)\rightarrow \text{translated up by 3 units} \rightarrow y=\log(2x)+3[/tex]
Therefore, Option 2 is correct.
It is compressed horizontally by a factor of 2 and translated up 3.
