Analyzing Increasing and Decreasing Functions from Graphs

The video tutorial explains how to determine the intervals where a function is increasing or decreasing and identifies any 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 definition of a function that is increasing?

• As x decreases, y increases.

• As x increases, y decreases.

• As x increases, y increases.

• As x decreases, y decreases.

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

• By calculating the second derivative.

• By tracing the graph from left to right and observing if it goes uphill or downhill.

• By tracing the graph from right to left.

• By checking the slope of the tangent line.

What does a high point on the graph represent?

• A relative minimum.

• A relative maximum.

• A point of inflection.

• A critical point.

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

• (2, 14)

• (-2, -18)

• (2, -14)

• (-2, 18)

What is the interval where the function is decreasing?

• From -2 to 2

• From 2 to infinity

• From -2 to -14

• From negative infinity to -2

What is the function value at the relative minimum?

• 2

• 18

• -2

• -14

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

• x is greater than -2

• x is greater than 2

• x is less than -2

• x is less than 2

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

• x is less than 2

• x is less than -2

• x is greater than 2

• x is greater than -2

What does the function do as you move right on the x-axis?

• Approaches negative infinity

• Oscillates

• Approaches positive infinity

• Remains constant

What is another term for a relative maximum?

• Absolute maximum

• Local maximum

• Global maximum

• Critical maximum