Ch. 2 - Graphs and Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 1

Chapter 3, Problem 1

Fill in the blank to correctly complete each sentence. The point (-1, 3) lies in quadrant ________ in the rectangular coordinate system.

Verified step by step guidance

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). Given the point (-1, 3), identify the quadrant by checking the signs of x = -1 and y = 3.

Verified video answer for a similar problem:

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

Video duration:

Key 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 number lines called axes: the x-axis (horizontal) and the y-axis (vertical). Points are located using ordered pairs (x, y), where x indicates horizontal position and y indicates vertical position.

Quadrants of the Coordinate Plane

The coordinate plane is divided into four quadrants numbered counterclockwise starting from the upper right. Quadrant I has positive x and y values, Quadrant II has negative x and positive y, Quadrant III has both x and y negative, and Quadrant IV has positive x and negative y.

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 x < 0 and y > 0 lies in Quadrant II. This method helps classify points based on their position relative to the axes.

Recommended video:

4:36

Determinants of 2×2 Matrices

Related Practice

Textbook Question

Fill in the blank(s) to correctly complete each sentence. The circle with equation $x^{2} + y^{2} = 49$ has center with coordinates________ and radius equal to__________ .

views

Textbook Question

Fill in the blank(s) to correctly complete each sentence. The domain of the relation { (3,5), (4, 9), (10, 13) } is _____.

Textbook Question

Without using paper and pencil, evaluate each expression given the following functions. $ƒ (x) = x + 1$ and $g (x) = x^{2}$

$(ƒ - g) (2)$

views

Textbook Question

Find the distance between each pair of points, and give the coordinates of the midpoint of the line segment joining them. P(3, -1), Q(-4, 5)

views

Textbook Question

To answer each question, refer to the following basic graphs. Which one is the graph of ƒ(x)=x²? What is its domain?

views

Textbook Question

Find the distance between each pair of points, and give the coordinates of the midpoint of the line segment joining them. M(-8, 2), N(3, -7)