Answer:
g(x) = |x – 0| – 5
Step-by-step explanation:
Given the parent absolute value function, f(x) = |x| :
The vertex of the parent absolute value function is (0, 0).
Hence, the translation of the parent absolute value function can be represented using the following vertex form:
g(x)= a|x – h| + k
Where:
(h, k) = vertex
a = determines whether the graph opens up or down.
h = determines how far left or right the parent function is translated.
k = determines how far up or down the parent function is translated.
The translation of 5 units down means that the vertex of g(x) is (0, -5). Substitute the value of the vertex, (0, -5) into the vertex form, we'll have the following equation that reflects the translation of the graph:
g(x)= |x – 0| – 5
**Note, the assumed value of a in the equation for g(x) is 1.
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