Question

Which of the following describes graphing y≥∣x−4∣?

a) Translate y=∣x∣ right 4 units and shade inside ∪

b) Translate y=∣x∣ down 4 units and shade inside ∪

c) Translate y=∣x∣ left 4 units and shade inside ∪

d) Translate y=∣x∣ right 4 units and shade inside ∩

Answer 1

The correct description is option d) Translate y=∣x∣ right 4 units and shade inside ∩.

Step-by-step explanation:

The correct description of graphing y ≥ ∣x−4∣ is option d) Translate y=∣x∣ right 4 units and shade inside ∩.

First, let's understand the graph of y = ∣x∣. It is a V-shaped graph that intersects the x-axis at (0, 0) and has the same value for y whether x is positive or negative.

To graph y = ∣x−4∣, we translate y = ∣x∣ 4 units to the right. This means that the graph will intersect the x-axis at (4, 0), and the V-shape will be centered at x = 4.

Finally, the inequality y ≥ ∣x−4∣ means that we need to shade the area above or on the graph. The symbol ∩ represents shading inside, so option d) is the correct choice.