Increasing and Decreasing Intervals of Polynomials

In the above graph complete the following end behavior:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

• -∞
  -∞

• +∞
  -∞

• -∞
  +∞

• +∞
  +∞

Where is the function decreasing?

• (-∞, -1)

• (-1, ∞)

• (-∞, 3)

• (-∞, ∞)

When is this function increasing?

• (-3, 3)

• (-2.5, 2.5)

• [-3, 3]

• (3, ∞)

What is the end behavior on the left side

• x →∞, y→∞

• x →-∞, y→-∞

• x →-∞, y→∞

• x →∞, y→∞

What is the End behavior on the right side

•  x→∞, y→∞

•  x→⁻∞, y→∞

•  x→⁻∞, y→0

•  x→∞, y→⁻∞

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 #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 #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, ∞).

For Graph #11, what is the interval where the function is decreasing?

• (3, 5)

• (-∞, 3)

• (5, ∞)

• (-∞, 5)

Answer explanation

The function is decreasing in the interval (3, 5) as indicated by the graph. In this range, the y-values of the function decrease as x increases, confirming that this is the correct interval for decreasing behavior.

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.