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

The second choice.

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 2

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

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.