Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

1. Equations & Inequalities

Linear Inequalities

College Algebra

1. Equations & Inequalities

Linear Inequalities

Previous problemNext problem

2:03 minutes

Problem 109

Textbook Question

In Exercises 107–110, use graphs to find each set. [1,3) ∩ (0,4)

Verified step by step guidance

Step 1: Understand the notation. The interval [1,3) means all numbers from 1 to 3, including 1 but not including 3. The interval (0,4) means all numbers greater than 0 and less than 4, excluding both 0 and 4.

Step 2: Represent each interval on a number line. For [1,3), draw a solid dot at 1 (to indicate inclusion) and an open circle at 3 (to indicate exclusion). For (0,4), draw open circles at both 0 and 4.

Step 3: Identify the intersection ∩ of the two intervals. The intersection represents the set of numbers that are common to both intervals.

Step 4: On the number line, observe where the two intervals overlap. The overlap starts at 1 (included because of [1,3)) and ends at 3 (excluded because of [1,3)).

Step 5: Write the result of the intersection as an interval. The intersection is [1,3), which includes all numbers from 1 to 3, including 1 but not including 3.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Interval Notation

Interval notation is a mathematical notation used to represent a range of values. It uses brackets and parentheses to indicate whether endpoints are included or excluded. For example, [1, 3) means that 1 is included in the interval, while 3 is not, indicating all numbers from 1 up to but not including 3.

Set Intersection

Set intersection refers to the operation of finding common elements between two sets. The intersection of sets A and B, denoted as A ∩ B, includes only those elements that are present in both sets. In the context of intervals, this means identifying the overlapping range of values that satisfy both conditions.

Graphing Intervals

Graphing intervals involves visually representing the range of values on a number line. Each interval is depicted with a line segment, where closed intervals are marked with solid dots and open intervals with open dots. This visual representation helps in easily identifying overlaps and intersections between different intervals.