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Ch. 5 - Systems and Matrices
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Lial 13th EditionCh. 5 - Systems and Matrices문제 62
6장, 문제 62

Graph the solution set of each system of inequalities.
y≤x3−xy\(\le\) x^3-x
y>−3y>-3

검증된 단계별 안내
1
Identify the two inequalities in the system: \(y \leq x^3 - x\) and \(y > -3\).
Graph the boundary curve for the first inequality, which is the cubic function \(y = x^3 - x\). Since the inequality is \(\leq\), include the curve itself as a solid line.
Shade the region below or on the curve \(y = x^3 - x\) because the inequality is \(y \leq x^3 - x\).
Graph the horizontal boundary line \(y = -3\). Since the inequality is strict (\(y > -3\)), draw this line as a dashed line to indicate points on the line are not included.
Shade the region above the line \(y = -3\) because the inequality is \(y > -3\). The solution set is the overlap of the shaded regions from both inequalities.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
7m
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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Graphing Inequalities

Graphing inequalities involves shading the region of the coordinate plane that satisfies the inequality. For example, y ≤ x³ - x means shading all points on or below the curve y = x³ - x. The boundary curve is included if the inequality is ≤ or ≥, and excluded if it is < or >.
추천 영상:
7:02
Linear Inequalities

Cubic Functions and Their Graphs

A cubic function like y = x³ - x has an S-shaped curve with turning points. Understanding its shape helps in accurately sketching the boundary for the inequality. Key features include intercepts, local maxima and minima, and end behavior as x approaches ±∞.
추천 영상:
5:26
Graphs of Logarithmic Functions

Systems of Inequalities

A system of inequalities requires finding the region where all inequalities overlap. For y ≤ x³ - x and y > -3, the solution set is the area below the cubic curve but above the line y = -3. The final graph shows the intersection of these shaded regions.
추천 영상:
6:19
Systems of Inequalities
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