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To get the function [tex]\( g \)[/tex], shift [tex]\( f \)[/tex] up/down by [tex]\(\square\)[/tex] units and to the right/left by [tex]\(\square\)[/tex] units.

[tex]\( f(x) = |x| \)[/tex]
[tex]\( g(x) = |x+9| - 5 \)[/tex]

Sagot :

GinnyAnswer
We start with the function [tex]\( f(x) = |x| \)[/tex], which is the absolute value function. To derive the function [tex]\( g(x) = |x + 9| - 5 \)[/tex], we need to apply a series of transformations to [tex]\( f(x) \)[/tex].

Let's analyze the transformations step by step:

1. Horizontal Shift:
The term [tex]\( |x + 9| \)[/tex] inside the absolute value indicates a horizontal shift. Since the expression is [tex]\( x + 9 \)[/tex], it means we shift the graph to the left by 9 units.

2. Vertical Shift:
The term [tex]\( -5 \)[/tex] outside the absolute value indicates a vertical shift. Subtracting 5 from the function shifts the graph downward by 5 units.

Thus, the function [tex]\( g(x) = |x + 9| - 5 \)[/tex] is obtained by shifting the function [tex]\( f(x) = |x| \)[/tex] down by 5 units and to the left by 9 units.

So to complete the description of the transformation for [tex]\( g \)[/tex]:

To get the function [tex]\( g \)[/tex], shift [tex]\( f \)[/tex] down by 5 units and to the left by 9 units.
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