Question

Which of the following functions would result in a graph that is shifted two
units to the left of g(x) = 3 log(x)?
A. f(x)=3 log(x-2)
B. f(x)=3 log(x) +2
C. f(x)=3 log(x+2)
D. f(x)=3 log(x) – 2

1. C. f(x)=3 log(x+2)
Step-by-step explanation:
Translations are forms that are transformations where the graph is shifted up, down, right, or left.
Horizontal Translation
The question asks for a translation of 2 units to the left. It is important to note that this is horizontal. All horizontal transformations will be written inside the parentheses. This is because transformations inside the parentheses affect the x-value, and the x-values are horizontal.
Writing Translations
All log functions are written as
• f(x) = a(log x – h) + k
The h and k values are responsible for all translations in this equation. We know to use the h-value for horizontal translations because of the information above.
Moving 2 to the left is moving –2 units. Since the left is closer to the negative side, if you go left, you subtract.
• f(x) = 3(log x – (-2))
This can be rewritten as
• f(x) = 3(log x + 2)
Since you are subtracting a negative, you can write it as addition.