Textbook Question
Graph each function. See Examples 6–8. _ ƒ(x) = 2√x + 1
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0. Review of College Algebra
Basics of Graphing
1:43 minutesProblem R.7.1
Textbook Question
CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. The point (-1, 3) lies in quadrant ________ in the rectangular coordinate system.
Verified step by step guidance1
Recall that the rectangular coordinate system is divided into four quadrants, each defined by the signs of the x and y coordinates.
Quadrant I contains points where both x and y are positive (x > 0, y > 0).
Quadrant II contains points where x is negative and y is positive (x < 0, y > 0).
Quadrant III contains points where both x and y are negative (x < 0, y < 0).
Quadrant IV contains points where x is positive and y is negative (x > 0, y < 0). Since the point (-1, 3) has x = -1 (negative) and y = 3 (positive), it lies in Quadrant II.
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Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Rectangular Coordinate System
The rectangular coordinate system, also known as the Cartesian plane, consists of two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). Points are represented as ordered pairs (x, y), where x indicates horizontal position and y indicates vertical position.
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Quadrants in the Coordinate Plane
The coordinate plane is divided into four quadrants numbered counterclockwise starting from the upper right: Quadrant I (+x, +y), Quadrant II (-x, +y), Quadrant III (-x, -y), and Quadrant IV (+x, -y). The sign of the coordinates determines the quadrant location.
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Determining the Quadrant of a Point
To find the quadrant of a point, examine the signs of its x and y coordinates. For example, a point with a negative x and positive y coordinate lies in Quadrant II. This method helps classify points based on their position relative to the axes.
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