Question

graph the equation. select integers for x from - 3 to 3, inclusive.
y = |x| - 5
choose the correct graph to the right.

Explanation:

Step1: Calculate y - values for given x - values

When \(x=-3\), \(y = |-3|-5=3 - 5=-2\); when \(x=-2\), \(y = |-2|-5=2 - 5=-3\); when \(x=-1\), \(y = |-1|-5=1 - 5=-4\); when \(x = 0\), \(y=|0|-5=-5\); when \(x = 1\), \(y = |1|-5=1 - 5=-4\); when \(x = 2\), \(y = |2|-5=2 - 5=-3\); when \(x = 3\), \(y = |3|-5=3 - 5=-2\).

Step2: Analyze the shape of the absolute - value function

The parent function of \(y = |x|\) is a V - shaped graph with the vertex at \((0,0)\). The function \(y = |x|-5\) is a vertical shift of the parent function \(y = |x|\) down 5 units. So the vertex of \(y = |x|-5\) is at \((0, - 5)\) and it opens upwards.

Answer:

The graph with a V - shape, vertex at \((0,-5)\) and passing through the points \((-3,-2),(-2,-3),(-1,-4),(1,-4),(2,-3),(3,-2)\) (assuming one of the options C has these characteristics as no specific details of options are given other than the layout of having 4 graphs to choose from). Without seeing the exact details of the graphs in A, B, C, D, based on the above - calculated points and the shape of the absolute - value function shifted down 5 units, the correct graph should have a V - shape opening upwards with vertex at \((0,-5)\).