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Suppose that [tex]$g(x) = f(x) + 6$[/tex]. Which statement best compares the graph of [tex]$g(x)$[/tex] with the graph of [tex][tex]$f(x)$[/tex][/tex]?

Sagot :

GinnyAnswer
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.
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