Question

What is the maximum and minimum value of y=∣x+4∣−3 on the interval [-2, 3]?

(a) Maximum: 1, Minimum: -7
(b) Maximum: -3, Minimum: 1
(c) Maximum: 7, Minimum: -1
(d) Maximum: -1, Minimum: 7

Answer 1

The maximum value of y=∣x+4∣−3 is 1 and the minimum value is -7.

Step-by-step explanation:

To find the maximum and minimum value of y=∣x+4∣−3 on the interval [-2, 3], we need to analyze the absolute value function. When the expression inside the absolute value is positive, the absolute value is equal to the expression itself. When the expression inside the absolute value is negative, the absolute value is equal to the negative of the expression.

So, for x ≤ -4, y = -(x+4) - 3.

For -4 < x ≤ 3, y = x+4 - 3.

For x > 3, y = x+4 - 3.

By evaluating these expressions at the endpoints of the interval [-2, 3], we find that the maximum value is 1 and the minimum value is -7. Therefore, the correct answer is (a) Maximum: 1, Minimum: -7.