Graph each inequality. y\u003e2x

Ch. 5 - Systems of Equations and Inequalities

Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경

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Blitzer 8th Edition

Ch. 5 - Systems of Equations and Inequalities

문제 23

6장, 문제 23

Graph each inequality. y>2^x

검증된 단계별 안내

Identify the inequality to graph: $y > 2^{x}$. This means we want to graph all points where the $y$-value is greater than \$2^{x}$.

First, graph the boundary curve $y = 2^{x}$. This is an exponential function where the base is 2, so it passes through points like $(0,1)$ since $2^{0} = 1$, and increases as $x$ increases.

Since the inequality is strict ($>$), draw the curve $y = 2^{x}$ as a dashed line to indicate that points on the line are not included in the solution.

Determine which side of the curve to shade by testing a point not on the curve, such as $(0,0)$. Substitute into the inequality: $0 > 2^{0}$ becomes $0 > 1$, which is false, so do not shade below the curve.

Shade the region above the curve $y = 2^{x}$, representing all points where $y$ is greater than \$2^{x}$.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

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주요 개념

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

Exponential Functions

An exponential function has the form y = a^x, where the base a is a positive constant. In this question, y = 2^x represents an exponential growth function, which increases rapidly as x increases. Understanding its shape and behavior is essential for graphing related inequalities.

Graphing Inequalities

Graphing an inequality like y > 2^x involves shading the region of the coordinate plane where the inequality holds true. The boundary curve y = 2^x is graphed first, and since the inequality is strict (greater than), the boundary is drawn as a dashed line to indicate points on the curve are not included.

Coordinate Plane and Regions

The coordinate plane is divided by the graph of the function into regions. For y > 2^x, the region above the curve is shaded. Understanding how to identify and shade the correct region based on the inequality symbol is crucial for accurately representing the solution set.

Graph each inequality. y>2x