The given function is g(x) = x| - 1.
To graph the function and the parent function, we first need to understand the parent function, which is the absolute value function, denoted as f(x) = |x|.
The parent function f(x) = |x| is a V-shaped graph that passes through the origin (0,0) and reflects any negative values of x to their positive counterparts. It has a slope of 1 on the right side of the origin and -1 on the left side.
To graph g(x) = x| - 1, we will modify the parent function by shifting it down by 1 unit:
1. For the parent function, plot points along the graph considering both positive and negative x-values. Connect the points to form a V-shape.
2. For g(x) = x| - 1, take the parent function and shift it down by 1 unit. Each point on the parent function will be shifted down vertically by 1 unit.
Here is a graph showing both the parent function f(x) = |x| (in blue) and the function g(x) = x| - 1 (in orange):
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| f(x) = | Apologies for the incomplete response. Here is the complete graph:
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| f(x) = |x|
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| g(x) = x| - 1
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The parent function f(x) = |x| is represented by the blue V-shaped graph, passing through the origin (0,0). The function g(x) = x| - 1 is represented by the orange graph, which is the parent function shifted down by 1 unit.
Note that the graph of g(x) = x| - 1 is the same as the parent function f(x) = |x|, except it is shifted downward by 1 unit.