Question

Which of the following points is the minimum of the graph of y = |x − 3| − 4 in the xy-plane?

Option 1: (3, -4)
Option 2: (0, -7)
Option 3: (6, 1)
Option 4: (2, 5)

Answer 1

The minimum of the graph y = |x − 3| − 4 is at the vertex of the V-shaped graph, which after shifting down by 4 units, is at Option 1: (3, -4).

Step-by-step explanation:

To determine which of the provided points is the minimum of the graph of y = |x − 3| − 4, we need to understand how the graph of an absolute value function behaves.

The function y = |x − 3| creates a V-shaped graph that has its vertex at the point where the expression inside the absolute value is zero. In this case, when x = 3, the expression inside the absolute value becomes zero. As a result, the vertex of the V-shaped graph is at the point (3, 0).

Now, we subtract 4 from the entire function to get y = |x − 3| − 4. This shifts the graph down by 4 units. Hence, the vertex of the graph now becomes (3, -4), which transforms it into the minimum point of the graph.

Therefore, the minimum of the graph of y = |x − 3| − 4 is Option 1: (3, -4).