Question

How is the graph y = log(2x)+3 related to the graph of y = log(x)? It is stretched horizontally by a factor of 2 and translated up 3. It is compressed horizontally by a factor of 2 and translated up 3. It is stretched vertically by a factor of 2 and translated up 3. It is compressed vertically by a factor of 2 and translated up 3.

Answer 1

Answer:

Option 2 - It is compressed horizontally by a factor of 2 and translated up 3.

Step-by-step explanation:

Given : The graph $y=\log(2x)+3$ and $y=\log(x)$  

To find : How does the graph of $y=\log(2x)+3$ related to the graph of $y=\log(x)$

Solution :  

The parent function be $y=\log(x)$

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 $y=\log(x) \rightarrow \text{Horizontally compressed by 2} \rightarrow y=\log(2x)$

Translated up :  

i.e, f(x)→f(x)+b  

Adding 3 means you are moving it up by 3 units  

$y=\log(2x)\rightarrow \text{translated up by 3 units} \rightarrow y=\log(2x)+3$  

Therefore, Option 2 is correct.

It is compressed horizontally by a factor of 2 and translated up 3.

Answer 2

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.