Question

How is the graph of y=log⁡(x) transformed to produce the graph of y=log⁡(2x)+3?

a) It is stretched horizontally by a factor of 2 and translated up 3 units.
b) It is compressed horizontally by a factor of 2 and translated up 3 units.
c) It is stretched vertically by a factor of 2 and translated up 3 units.
d) It is compressed vertically by a factor of 2 and translated up 3 units.

Answer 1

The graph y=log(x) is transformed into y=log(2x)+3 by compressing it horizontally by a factor of 2 and then translating it upwards by 3 units.

Step-by-step explanation:

The transformation from the graph of y=log(x) to the graph of y=log(2x)+3 involves two changes. First, the presence of the term 2x inside the logarithm indicates a horizontal compression by a factor of 2 because for any given y-value, the x-value that produces it has been halved. Second, the addition of +3 outside the logarithm indicates a vertical translation upwards by 3 units. Therefore, the correct transformation is option b) It is compressed horizontally by a factor of 2 and translated up 3 units.