Using the absolute value function, we have that:
1) The table is:
2) The graph is given at the end of the answer.
3) The rule is: g(x) = |x - 3|.
4) The rule is: D(x) = |x| - 5.
5) The rule is: K(x) = |x - 3| - 5.
What is the absolute value function?
The absolute function is defined by:
It measures the distance of a point x to the origin.
Hence, applying the rule, the table is completed as follows:
The function is graphed at the end of the answer.
A translation right of 3 units is given by:
f(x - 3).
Hence:
g(x) = |x - 3|.
A translation down 5 units is given by:
f(x) - 5.
Hence:
D(x) = |x| - 5.
For item 5, the function was shifted 5 units down and 3 right, hence it is given by:
K(x) = |x - 3| - 5.
More can be learned about the absolute value function at https://brainly.com/question/24734454
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