Understanding Interval Notation for Graphs

What does it mean for a graph to be increasing?

• The graph remains flat as you read from left to right.

• The graph moves upwards as you read from left to right.

• The graph has a constant negative slope.

• The graph moves downwards as you read from left to right.

Why should endpoints not be included in interval notation?

• Endpoints are only included if the graph is constant.

• Endpoints are irrelevant to interval notation.

• Endpoints indicate a change in the graph's direction.

• Endpoints are always included in interval notation.

In the first example, what is the interval where the graph is increasing?

• From negative infinity to 1

• From 0 to 1

• From 1 to positive infinity

• From -1 to positive infinity

In the first example, what is the interval where the graph is decreasing?

• From -1 to positive infinity

• From 1 to positive infinity

• From negative infinity to -1

• From 0 to 1

In the second example, what is the interval where the graph is constant?

• From 0 to 1

• From 2 to positive infinity

• From negative infinity to 1

• From 1 to 2

In the third example, which intervals are increasing?

• From 1 to 2 and from 2 onward

• From -1 to 0 and from 1 onward

• From 0 to 1 and from 2 onward

• From negative infinity to -1 and from 0 to 1

In the third example, which intervals are decreasing?

• From negative infinity to -1 and from 0 to 1

• From 1 to 2 and from 2 onward

• From 0 to 1 and from 1 to 2

• From -1 to 0 and from 1 onward

In the final examples, what is the significance of asymptotes?

• They are points where the graph changes direction.

• They represent boundaries the graph approaches but never touches.

• They show where the graph crosses the x-axis.

• They indicate where the graph is constant.

In the final examples, what is the interval where the graph is increasing?

• From negative infinity to 1 and from 1 to 2

• From 0 to 1 and from 1 to 2

• From negative infinity to 2 and from 2 to positive infinity

• From 2 to positive infinity

In the final examples, is there any interval where the graph is decreasing?

• Yes, from negative infinity to 0

• No, the graph is never decreasing

• Yes, from 1 to 2

• Yes, from 0 to 1