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0. Fundamental Concepts of Algebra3h 32m
1. Equations and Inequalities3h 27m
2. Graphs1h 43m
3. Functions & Graphs2h 17m
4. Polynomial Functions1h 54m
5. Rational Functions1h 23m
6. Exponential and Logarithmic Functions2h 28m
7. Measuring Angles40m
8. Trigonometric Functions on Right Triangles2h 5m
9. Unit Circle1h 19m
10. Graphing Trigonometric Functions1h 19m
11. Inverse Trigonometric Functions and Basic Trig Equations1h 41m
12. Trigonometric Identities 2h 34m
13. Non-Right Triangles1h 38m
14. Vectors2h 25m
15. Polar Equations2h 5m
16. Parametric Equations1h 6m
17. Graphing Complex Numbers1h 7m
18. Systems of Equations and Matrices3h 6m
19. Conic Sections2h 36m
20. Sequences, Series & Induction1h 15m
21. Combinatorics and Probability1h 45m
22. Limits & Continuity1h 49m
23. Intro to Derivatives & Area Under the Curve2h 9m

1. Equations and Inequalities

Linear Inequalities

Precalculus

1. Equations and inequalities

Linear Inequalities

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Multiple Choice

Express the given interval in set builder notation and graph. (−∞, 0]

{ $x\left|x\right.$ ≤ 0}

Number line with a graph

{ $x\left|x\right.$ < 0}

Number line with a graph

{ $x\left|x\right.$ > 0}

Number line with a graph

$\left\lbrace x|x\ge0\right\rbrace$

Number line with a graph

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Verified step by step guidance

Identify the given interval: The interval is (−∞, 0], which means it includes all numbers less than or equal to 0.

Understand the notation: The round parenthesis '(' indicates that −∞ is not included in the interval, while the square bracket ']' indicates that 0 is included.

Express in set builder notation: The interval (−∞, 0] can be expressed as {x | x ≤ 0}, which reads as 'the set of all x such that x is less than or equal to 0.'

Graph the interval: On a number line, draw a line extending to the left from 0, with a closed dot at 0 to indicate that 0 is included in the interval.

Review the graph: Ensure that the line extends indefinitely to the left, representing all numbers less than 0, and that the closed dot at 0 correctly shows inclusion of 0 in the interval.