Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 2.2, Problem 62STP
To determine

To state: the domain and range of relation. Then determine whether relation is a function, if it is determine if it is one-to-one, onto, both , or neither.

Expert Solution & Answer
Check Mark

Answer to Problem 62STP

Domain and Range are all real numbers.

The relation is a function.

The function is one-to-one and onto.

Explanation of Solution

Given information:

  Algebra 2, Chapter 2.2, Problem 62STP

Formula used:

A function is a relation in which each element of the domain is paired with exactly one element in the range.

One-to −One function: Each element of the domain pairs exactly one unique element of the range.

Onto function: Each element of the range corresponds to an element of the domain.

Vertical−Test: If no vertical line intersects a graph in more than one point, the graph represents a function whereas if vertical line intersects a graph more than one point ,the graph does not represent a function.

Calculation:

According to the question ,

Every real number is the x -coordinate of points showed in graph and every real number is

y -coordinate of points showed in graph.

So, the domain and range are both all real numbers.

The graph passes the vertical test. Therefore, it is a function.

The graph shows the following coordinates:

  (2,3);(1,5);(2,3);(4,1)

Every x -value is paired with exactly one unique y -value, and every y -value corresponds to an x -value.

Thus, the function is both one-to-one and onto.

Chapter 2 Solutions

Algebra 2

Ch. 2.1 - Prob. 5CYUCh. 2.1 - Prob. 6CYUCh. 2.1 - Prob. 7CYUCh. 2.1 - Prob. 8CYUCh. 2.1 - Prob. 9CYUCh. 2.1 - Prob. 10CYUCh. 2.1 - Prob. 11PPSCh. 2.1 - Prob. 12PPSCh. 2.1 - Prob. 13PPSCh. 2.1 - Prob. 14PPSCh. 2.1 - Prob. 15PPSCh. 2.1 - Prob. 16PPSCh. 2.1 - Prob. 17PPSCh. 2.1 - Prob. 18PPSCh. 2.1 - Prob. 19PPSCh. 2.1 - Prob. 20PPSCh. 2.1 - Prob. 21PPSCh. 2.1 - Prob. 22PPSCh. 2.1 - Prob. 23PPSCh. 2.1 - Prob. 24PPSCh. 2.1 - Prob. 25PPSCh. 2.1 - Prob. 26PPSCh. 2.1 - Prob. 27PPSCh. 2.1 - Prob. 28PPSCh. 2.1 - Prob. 29PPSCh. 2.1 - Prob. 30PPSCh. 2.1 - Prob. 31PPSCh. 2.1 - Prob. 32PPSCh. 2.1 - Prob. 33PPSCh. 2.1 - Prob. 34PPSCh. 2.1 - Prob. 35HPCh. 2.1 - Prob. 36HPCh. 2.1 - Prob. 37HPCh. 2.1 - Prob. 38HPCh. 2.1 - Prob. 39HPCh. 2.1 - Prob. 40HPCh. 2.1 - Prob. 41HPCh. 2.1 - Prob. 42HPCh. 2.1 - Prob. 43HPCh. 2.1 - Prob. 44HPCh. 2.1 - Prob. 45STPCh. 2.1 - Prob. 46STPCh. 2.1 - Prob. 47STPCh. 2.1 - Prob. 48STPCh. 2.1 - Prob. 49STPCh. 2.1 - Prob. 50STPCh. 2.1 - Prob. 51STPCh. 2.1 - Prob. 52STPCh. 2.1 - 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