Identifying Increasing and Decreasing Intervals in Functions

The video tutorial explains the concepts of increasing and decreasing intervals in functions. It begins with definitions, followed by example problems to illustrate these concepts. The tutorial also introduces the tangent line method to determine intervals and provides a step-by-step approach to solving problems. The focus is on identifying intervals where functions increase or decrease, using both algebraic and calculus perspectives.

What is an increasing interval?

• When X values decrease and Y values increase.

• When X values increase and Y values increase.

• When X values increase and Y values decrease.

• When both X and Y values decrease.

What happens to the Y value in a decreasing interval as X increases?

• Y value increases.

• Y value decreases.

• Y value remains constant.

• Y value oscillates.

In the interval from -5 to -4, what happens to the Y values?

• Y values increase.

• Y values decrease.

• Y values remain constant.

• Y values oscillate.

Which interval is increasing from the given options?

• From -4 to -3

• From -2 to 2

• From -5 to -4

• From 3 to 4

How can you confirm an interval is increasing using a tangent line?

• The tangent line is horizontal.

• The tangent line is vertical.

• The tangent line has a negative slope.

• The tangent line has a positive slope.

What is the slope of the tangent line at a peak or valley?

• Undefined

• Zero

• Negative

• Positive

In the interval from -1 to 0, what happens to the Y values?

• Y values oscillate.

• Y values remain constant.

• Y values decrease.

• Y values increase.

Which interval is decreasing from the given options?

• From 0 to 2

• From 3.5 to 4.5

• From -2 to 0

• From -1 to 0

What is the correct interval where the function H(x) is increasing?

• From -5 to -3

• From 3 to 4

• From -2 to 0

• From 0 to 2

What is the correct interval where the function G(x) is decreasing?

• From -1 to 0

• From 3 to 4

• From -5 to -4

• From -2 to 2