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Which direction must the graph of [tex]$f(x)=|x|$[/tex] be shifted to produce the graph of [tex]$g(x)=|x|-9$[/tex]?

A. left
B. right
C. down
D. up

Sagot :

GinnyAnswer
To determine how the graph of [tex]\( f(x) = |x| \)[/tex] needs to be shifted to produce the graph of [tex]\( g(x) = |x| - 9 \)[/tex], let’s analyze the transformations applied to [tex]\( f(x) \)[/tex]:

1. The function [tex]\( f(x) = |x| \)[/tex] represents the absolute value function, which has its vertex at the origin (0,0) and opens upwards.

2. The function [tex]\( g(x) = |x| - 9 \)[/tex] can be understood as the absolute value function [tex]\( f(x) = |x| \)[/tex], but with a vertical shift.

3. To see how the graph shifts:

- Start with [tex]\( f(x) \)[/tex]:
[tex]\[ f(x) = |x| \][/tex]

- Compare it with [tex]\( g(x) \)[/tex]:
[tex]\[ g(x) = |x| - 9 \][/tex]

- The term [tex]\(-9\)[/tex] indicates that each point on the graph of [tex]\( f(x) = |x| \)[/tex] is moved vertically downward by 9 units.

Therefore, to transform the graph of [tex]\( f(x) = |x| \)[/tex] to [tex]\( g(x) = |x| - 9 \)[/tex], you must shift the graph downward.

Thus, the correct direction is "down", which corresponds to choice:

C. down
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