Determining Intervals Over Which a Function is Increasing (3.7.1)

Question 1

• A function is decreasing if the graph drops as the x-values get larger.

Answer 1

• A function is decreasing if the graph drops as the x-values get larger.

Question 2

• A function is increasing if the graph rises as the x-values get larger.

Answer 2

• A function is increasing if the graph rises as the x-values get larger.

Question 3

• A function is constant if it is neither increasing nor decreasing over a given interval.

Answer 3

• A function is constant if it is neither increasing nor decreasing over a given interval.

Question 4

• A maximum is a high point that occurs when an increasing curve begins decreasing.

Answer 4

• A maximum is a high point that occurs when an increasing curve begins decreasing.

Question 5

• A minimum is a low point that occurs when a decreasing curve begins increasing.

Answer 5

• A minimum is a low point that occurs when a decreasing curve begins increasing.

Question 6

• Whether a function is increasing or decreasing is determined as the graph is viewed from left to right.

Answer 6

• Whether a function is increasing or decreasing is determined as the graph is viewed from left to right.

Question 7

• Some functions increase and decrease many times over their curve.

Answer 7

• Some functions increase and decrease many times over their curve.

Question 8

This function is decreasing for all the x-values smaller than
0. As you view the portion of the curve to the left of the
y-axis, reading it from left to right, it is falling.
The function is increasing for all x-values larger than 0. As
you view the portion of the curve to the right of the y-axis,
reading it also from left to right, it is rising.
The point where the curve turns is a minimum.
This function is always decreasing. Remember to read the
curve from left to right as you make your judgement.
It has no maximum or minimum points because it never turns.
This function is increasing for all x-values less than +2.
The function is decreasing for all x-values greater than +2.
This function is always constant. It neither rises nor falls.

Answer 8

This function is decreasing for all the x-values smaller than
0. As you view the portion of the curve to the left of the
y-axis, reading it from left to right, it is falling.
The function is increasing for all x-values larger than 0. As
you view the portion of the curve to the right of the y-axis,
reading it also from left to right, it is rising.
The point where the curve turns is a minimum.
This function is always decreasing. Remember to read the
curve from left to right as you make your judgement.
It has no maximum or minimum points because it never turns.
This function is increasing for all x-values less than +2.
The function is decreasing for all x-values greater than +2.
This function is always constant. It neither rises nor falls.

Question 9

This function is constant for all x-values less than or equal
to 0. It is also constant for all x-values greater than or equal
to 3.
The function is decreasing over the interval 0

Answer 9

This function is constant for all x-values less than or equal
to 0. It is also constant for all x-values greater than or equal
to 3.
The function is decreasing over the interval 0