Question

graphing a logarithmic function after a transformation

the graph of \\(f(x) = \log x + 3\\) is the graph of \\(g(x) = \log x\\) translated 3 units

Explanation:

Identify the relationship between the functions

Using the Vertical Translation and Exponential Function Transformations knowledge points

$$ f(x) = g(x) + c \implies f(x) = \log x + 3 $$

Determine the direction of the translation

Using the Vertical Translation knowledge point

$$ c = 3 > 0 \implies \text{translated } 3 \text{ units up} $$

Answer:

The graph of \(f(x) = \log x + 3\) is the graph of \(g(x) = \log x\) translated 3 units <blank>up</blank>.