Question

Which of the following describes graphing y ≥ |x| - 4? A. Translate y = |x| down 4 units and shade inside the V. B. Translate y = |x| right 4 units and shade inside the V. C. Translate y = |x| left 4 units and shade inside the V. D. Translate y = |x| up 4 units and shade inside the V.

Answer 1

The inequality y ≥ |x| - 4 describes all the points above or on the graph of the equation y = |x| - 4.

To graph y = |x| - 4, we can start by plotting the points where x = 0, x = -1, and x = 1:

When x = 0, y = |0| - 4 = -4, so the point (0, -4) is on the graph.
When x = -1, y = |-1| - 4 = -3, so the point (-1, -3) is on the graph.
When x = 1, y = |1| - 4 = -3, so the point (1, -3) is on the graph.

Plotting these points and connecting them with a V-shaped curve, we get the graph of y = |x| - 4.

To shade the region above or on the graph of y = |x| - 4, we can shade the inside of the V-shaped curve.

Therefore, the correct answer is A. Translate y = |x| down 4 units and shade inside the V.