/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 115 Explain how to identify the doma... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 115

Explain how to identify the domain and range of a function from its graph.

Short Answer

Expert verified
In order to identify the domain and range of a function from its graph, one needs to find the furthest points of the graph along the x-axis (domain) and y-axis (range). If the line of the graph continues indefinitely in certain directions, this will be represented as 鈭� or -鈭� in the domain or range accordingly.

Step by step solution

01

Understanding Domain and Range

Domain is defined as the set of all possible input values (usually x), that the function can accept. If it's a graphical representation, domain is the measure from left to right along the x-axis that the graph occupies. Meanwhile, Range is defined as the set of all possible output values (usually y), that the function can produce. This is the measure from down to up along the y-axis that the function鈥檚 graph occupies.
02

Identifying the Domain

Visually examine the graph and determine the furthest points to the left and right, along the x-axis, where the graph exists. These will give approximate minimum and maximum values. If an arrow is present on the graph line, indicating that the graph continues indefinitely in that direction, the domain will either be (-鈭�, a] or [a, 鈭�) or if both ends have arrows, it will be (-鈭�, 鈭�). a here represents the x-coordinate of the endpoint if it exists.
03

Identifying the Range

Analogously to the Domain, visually examine the graph and determine the lowest and highest points, along the y-axis, where the graph exists. This will give approximate minimum and maximum values. If an arrow is present on the graph line, indicating that the graph continues indefinitely in that direction the range will either be (-鈭�, b] or [b, 鈭�) or if both ends have arrows, it will be (-鈭�, 鈭�). b here represents the y-coordinate of the endpoint, if it exists.

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