Understanding Function Intervals and Extrema

The video tutorial explains how to determine the intervals where a function is increasing or decreasing and identifies relative extrema. It describes how to trace a graph to find these intervals and highlights the importance of relative maxima and minima. The tutorial also covers how to express intervals using both interval notation and inequalities.

What is the formal definition of a function being increasing?

• As x decreases, y decreases.

• As x decreases, y increases.

• As x increases, y increases.

• As x increases, y decreases.

How can you determine if a function is decreasing by tracing the graph?

• By moving uphill from right to left.

• By moving uphill from left to right.

• By moving downhill from left to right.

• By moving downhill from right to left.

What are the coordinates of the relative maximum point mentioned in the video?

• (2, -14)

• (2, 18)

• (-2, 18)

• (-2, -14)

At which x-value does the function change from increasing to decreasing?

• x = 1

• x = 2

• x = -2

• x = 0

What is the function value at the local minimum point?

• 18

• -14

• 14

• 0

What is the interval notation for a function increasing from 2 to infinity?

• [2, infinity]

• (2, infinity]

• [2, infinity)

• (2, infinity)

What is another term for a relative maximum?

• Absolute maximum

• Local minimum

• Local maximum

• Absolute minimum

Which interval notation represents a function decreasing from -2 to 2?

• [-2, 2)

• (-2, 2)

• [-2, 2]

• (-2, 2]

How is the interval from negative infinity to -2 expressed using inequalities?

• x <= -2

• x >= -2

• x < -2

• x > -2

What happens to the function as you move right on the x-axis?

• It approaches negative infinity.

• It approaches zero.

• It approaches positive infinity.

• It remains constant.