Question

Observe the graph given below and answer the question that follows.

Statement 1: f(x) increases in (−∞,-1) and (1, ∞)

Statement 2: f(x) decreases in (−∞, 0) and (1, ∞)

Which one of the following is correct?

Options

• Statement 1 is true and Statement 2 is false.

• Statement 2 is true and Statement 1 is false.

• Both the statements are true.

• Both the statements are false.

Answer 1

Both the statements are false.

Explanation:

• Statement 1 is False: Looking at the graph, it actually decreases (goes down) in the interval (−∞, −1). it only increases in (−1, 0) and (1, ∞)
• Statement 2 is False: f(x) does not decrease across the entire (−∞, 0) range; it decreases from but then increases from (−1, 0). Similarly, it increases in (1, ∞) rather than decreasing.