Sure! Given the functions [tex]\( g(x) = f(x) + 6 \)[/tex], we need to compare the graphs of [tex]\( g(x) \)[/tex] and [tex]\( f(x) \)[/tex].
1. The function [tex]\( g(x) = f(x) + 6 \)[/tex] can be viewed as [tex]\( f(x) \)[/tex] with an additional constant value added to it.
2. Adding a constant value to a function results in a vertical shift of the graph of the original function. In this case, adding [tex]\( 6 \)[/tex] means that every output value of [tex]\( f(x) \)[/tex] is increased by [tex]\( 6 \)[/tex].
3. Therefore, the graph of [tex]\( g(x) \)[/tex] is exactly the same as the graph of [tex]\( f(x) \)[/tex], but every point on the graph of [tex]\( f(x) \)[/tex] is moved [tex]\( 6 \)[/tex] units upwards on the y-axis.
To summarize, the statement that best compares the graph of [tex]\( g(x) \)[/tex] with the graph of [tex]\( f(x) \)[/tex] is:
- The graph of [tex]\( g(x) \)[/tex] is the graph of [tex]\( f(x) \)[/tex] shifted 6 units upwards.
