Question

Compared to the parent function of f(x) = log(x), how has the graph of f(x) = 3log(x + 2) - 6 been transformed?

a) Shifted 3 units up and 2 units to the left
b) Shifted 3 units down and 2 units to the right
c) Shifted 2 units up and 3 units to the left
d) Shifted 2 units down and 3 units to the right

Answer 1

The correct transformation of the function f(x) = 3log(x + 2) - 6 compared to f(x) = log(x) is option (b): Shifted 3 units down and 2 units to the right.

Step-by-step explanation:

The function f(x) = 3log(x + 2) - 6 compared to the parent function f(x) = log(x), has been transformed as follows:

• The addition of 2 inside the logarithm (x + 2) indicates a horizontal shift to the left by 2 units.
• The multiplication by 3 outside the logarithm indicates a vertical stretch by a factor of 3.
• The subtraction of 6 from the entire function indicates a vertical shift downward by 6 units.

Therefore, the correct transformation is option (b): Shifted 3 units down and 2 units to the right.