Increasing/Decreasing Intervals from Polynomials

For Graph #1, over which interval is the function increasing?

• (-∞, 2)

• (2, ∞)

• (4, 6)

• (0, 2)

Answer explanation

The function is increasing in the interval (2, ∞) as the graph shows a positive slope beyond x = 2. The other intervals either have a negative slope or are not applicable.

For Graph #2, over which interval is the function decreasing?

• (4, 6)

• (2, ∞)

• (0, 2)

• (-∞, 4)

Answer explanation

The function is decreasing in the interval (4, 6) as the graph shows a downward trend in this range. Other intervals do not exhibit a decrease.

For Graph #3, over which interval is the function increasing?

• (0, 2)

• (-∞, 0) ∪ (2, ∞)

• (2, ∞)

• (4, 6)

Answer explanation

The function is increasing in the intervals where the slope is positive. In Graph #3, the function increases from (-∞, 0) and again from (2, ∞), making the correct answer (-∞, 0) ∪ (2, ∞).

For Graph #4, over which interval is the function decreasing?

• (2, ∞)

• (-∞, 2)

• (0, 2)

• (4, 6)

Answer explanation

The function is decreasing in the interval (2, ∞) as the graph shows a downward trend starting from x = 2 and continuing indefinitely. The other intervals do not reflect a decreasing behavior.

What is the interval of increase for Graph #5?

• (3, 5)

• (-∞, 3)

• (5, ∞)

• (-∞, 5)

Answer explanation

The interval of increase for Graph #5 is (3, 5) because the graph rises between these x-values. The function is increasing in this range, while it decreases outside of it.

What is the interval of decrease for Graph #6?

• (-∞, -3)

• (-3, ∞)

• (0, 3)

• (3, ∞)

Answer explanation

Graph #6 decreases on the interval (-∞, -3) because the function values are falling as x approaches -3 from the left. Beyond -3, the graph may increase or remain constant.

What is the interval of increase for Graph #7?

• (-∞, -3)

• (-3, ∞)

• (0, 3)

• (3, ∞)

Answer explanation

Graph #7 increases on the interval (-∞, -3) because the function values rise as x approaches -3 from the left. The other intervals do not show an increase in function values.

What is the interval of decrease for Graph #8?

• (-∞, 0) ∪ (2, ∞)

• (0, 2)

• (-∞, 2)

• (2, ∞)

Answer explanation

Graph #8 decreases in the intervals where the slope is negative. Analyzing the graph, it decreases from -∞ to 0 and from 2 to ∞, confirming the correct choice is (-∞, 0) ∪ (2, ∞).

For Graph #9, what is the interval where the function is increasing?

• (-1, 0) ∪ (1, ∞)

• (-∞, -1) ∪ (0, 1)

• (-∞, 0) ∪ (1, ∞)

• (0, 1) ∪ (1, ∞)

Answer explanation

The function is increasing in the intervals where the slope is positive. For Graph #9, this occurs in the intervals (-1, 0) and (1, ∞), making the correct answer (-1, 0) ∪ (1, ∞).

For Graph #10, what is the interval where the function is decreasing?

• (-1, 0) ∪ (1, ∞)

• (-∞, -1) ∪ (0, 1)

• (-∞, 0) ∪ (1, ∞)

• (0, 1) ∪ (1, ∞)

Answer explanation

The function is decreasing in the intervals where the slope is negative. For Graph #10, this occurs in the intervals (-1, 0) and (1, ∞), making the correct answer (-1, 0) ∪ (1, ∞).