Question

The parent function h(x)=log3(x) is transformed into j(x)=2log3(x+3)−7. Using complete sentences, describe ALL transformation that occurred.

Answer 1

• The function is vertically scaled (expanded) by a factor of 2.
• The scaled function is translated left 3 units and down 7 units.

Explanation:

When a function f(x) is transformed by ...

g(x) = a·f(x -h) +k

it has been vertically scaled by a factor of "a" and translated to the right and up by amounts h and k, respectively.

Here, we have a=2, h=-3, and k=-7. The means ...

The function has been vertically expanded by a factor of 2, translated left 3 units, and translated down 7 units.