Intermediate Algebra
10th Edition
ISBN: 9781285195728
Author: Jerome E. Kaufmann, Karen L. Schwitters
Publisher: Cengage Learning
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Chapter 9.3, Problem 4CQ
To determine
To match:
The function 
with the description of its graph relative to the graph of 
.
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Question 1. Solve the system
-
x1 x2 + 3x3 + 2x4
-x1 + x22x3 + x4
2x12x2+7x3+7x4
Question 2. Consider the system
= 1
=-2
= 1
3x1 - x2 + ax3
= 1
x1 + 3x2 + 2x3
x12x2+2x3
= -b
= 4
1 For what values of a, b will the system be inconsistent?
2 For what values of a, b will the system have only one solution?
For what values of a, b will the saystem have infinitely many solutions?
Chapter 9 Solutions
Intermediate Algebra
Ch. 9.1 - For Problems 110, answer true or false. A function...Ch. 9.1 - Prob. 2CQCh. 9.1 - Prob. 3CQCh. 9.1 - Prob. 4CQCh. 9.1 - Prob. 5CQCh. 9.1 - Prob. 6CQCh. 9.1 - Prob. 7CQCh. 9.1 - Prob. 8CQCh. 9.1 - Prob. 9CQCh. 9.1 - Prob. 10CQ
Ch. 9.1 - Prob. 1PSCh. 9.1 - Prob. 2PSCh. 9.1 - Prob. 3PSCh. 9.1 - Prob. 4PSCh. 9.1 - Prob. 5PSCh. 9.1 - Prob. 6PSCh. 9.1 - Prob. 7PSCh. 9.1 - Prob. 8PSCh. 9.1 - Prob. 9PSCh. 9.1 - Prob. 10PSCh. 9.1 - Prob. 11PSCh. 9.1 - Prob. 12PSCh. 9.1 - Prob. 13PSCh. 9.1 - Prob. 14PSCh. 9.1 - Prob. 15PSCh. 9.1 - Prob. 16PSCh. 9.1 - Prob. 17PSCh. 9.1 - Prob. 18PSCh. 9.1 - Prob. 19PSCh. 9.1 - Prob. 20PSCh. 9.1 - Prob. 21PSCh. 9.1 - Prob. 22PSCh. 9.1 - Prob. 23PSCh. 9.1 - Prob. 24PSCh. 9.1 - Prob. 25PSCh. 9.1 - Prob. 26PSCh. 9.1 - Prob. 27PSCh. 9.1 - Prob. 28PSCh. 9.1 - Prob. 29PSCh. 9.1 - Prob. 30PSCh. 9.1 - Prob. 31PSCh. 9.1 - Prob. 32PSCh. 9.1 - Prob. 33PSCh. 9.1 - Prob. 34PSCh. 9.1 - Prob. 35PSCh. 9.1 - Prob. 36PSCh. 9.1 - Prob. 37PSCh. 9.1 - Prob. 38PSCh. 9.1 - Prob. 39PSCh. 9.1 - Prob. 40PSCh. 9.1 - Prob. 41PSCh. 9.1 - Prob. 42PSCh. 9.1 - Prob. 43PSCh. 9.1 - Prob. 44PSCh. 9.1 - Prob. 45PSCh. 9.1 - Prob. 46PSCh. 9.1 - Prob. 47PSCh. 9.1 - Prob. 48PSCh. 9.1 - Prob. 49PSCh. 9.1 - Prob. 50PSCh. 9.1 - Prob. 51PSCh. 9.1 - Prob. 52PSCh. 9.1 - Prob. 53PSCh. 9.1 - Prob. 54PSCh. 9.1 - Prob. 55PSCh. 9.1 - Prob. 56PSCh. 9.1 - If f(x)=3|x|1 and g(x)=|x|+1, find f(2), f(3),...Ch. 9.1 - Prob. 58PSCh. 9.1 - Prob. 59PSCh. 9.1 - Prob. 60PSCh. 9.1 - Prob. 61PSCh. 9.1 - Prob. 62PSCh. 9.1 - Prob. 63PSCh. 9.1 - Prob. 64PSCh. 9.1 - Prob. 65PSCh. 9.1 - Prob. 66PSCh. 9.1 - The height of a projectile fired vertically into...Ch. 9.1 - Prob. 68PSCh. 9.1 - Acar rental agency 50 per day plus 0.32 a mile....Ch. 9.1 - Prob. 70PSCh. 9.1 - The equation I(r)=500r expresses the amount of...Ch. 9.1 - Prob. 72PSCh. 9.1 - Prob. 73PSCh. 9.1 - Prob. 74PSCh. 9.1 - Prob. 75PSCh. 9.1 - Prob. 76PSCh. 9.1 - Prob. 77PSCh. 9.2 - For Problems 110, answer true or false. The...Ch. 9.2 - Prob. 2CQCh. 9.2 - For problems 110, answer true or false. The graph...Ch. 9.2 - Prob. 4CQCh. 9.2 - Prob. 5CQCh. 9.2 - Prob. 6CQCh. 9.2 - Prob. 7CQCh. 9.2 - Prob. 8CQCh. 9.2 - Prob. 9CQCh. 9.2 - Prob. 10CQCh. 9.2 - Prob. 1PSCh. 9.2 - Prob. 2PSCh. 9.2 - Prob. 3PSCh. 9.2 - Prob. 4PSCh. 9.2 - Prob. 5PSCh. 9.2 - Prob. 6PSCh. 9.2 - Prob. 7PSCh. 9.2 - Prob. 8PSCh. 9.2 - Prob. 9PSCh. 9.2 - Prob. 10PSCh. 9.2 - Prob. 11PSCh. 9.2 - Prob. 12PSCh. 9.2 - Prob. 13PSCh. 9.2 - Prob. 14PSCh. 9.2 - Prob. 15PSCh. 9.2 - Prob. 16PSCh. 9.2 - Prob. 17PSCh. 9.2 - Prob. 18PSCh. 9.2 - Prob. 19PSCh. 9.2 - Prob. 20PSCh. 9.2 - Prob. 21PSCh. 9.2 - Prob. 22PSCh. 9.2 - Prob. 23PSCh. 9.2 - Prob. 24PSCh. 9.2 - Prob. 25PSCh. 9.2 - Prob. 26PSCh. 9.2 - Prob. 27PSCh. 9.2 - Prob. 28PSCh. 9.2 - Prob. 29PSCh. 9.2 - Prob. 30PSCh. 9.2 - Prob. 31PSCh. 9.2 - Prob. 32PSCh. 9.2 - Prob. 33PSCh. 9.2 - Prob. 34PSCh. 9.2 - To solve Problems 3544, use linear functions....Ch. 9.2 - Prob. 36PSCh. 9.2 - Prob. 37PSCh. 9.2 - Prob. 38PSCh. 9.2 - Prob. 39PSCh. 9.2 - To solve Problems 3544, use linear functions....Ch. 9.2 - Prob. 41PSCh. 9.2 - Prob. 42PSCh. 9.2 - Prob. 43PSCh. 9.2 - Prob. 44PSCh. 9.2 - Prob. 45PSCh. 9.2 - Prob. 46PSCh. 9.2 - Prob. 47PSCh. 9.2 - Prob. 48PSCh. 9.2 - Prob. 49PSCh. 9.2 - Prob. 50PSCh. 9.2 - Prob. 51PSCh. 9.2 - A specialty bicycle manufacturer has determined...Ch. 9.2 - Prob. 53PSCh. 9.2 - Prob. 54PSCh. 9.2 - Prob. 55PSCh. 9.2 - Prob. 56PSCh. 9.2 - Thoughts Into Words Suppose that Bianca walks at a...Ch. 9.2 - Use a graphing calculator to check your graphs for...Ch. 9.2 - Prob. 59.1PSCh. 9.2 - Prob. 59.2PSCh. 9.2 - Prob. 59.3PSCh. 9.2 - Prob. 59.4PSCh. 9.2 - Prob. 59.5PSCh. 9.2 - Prob. 60PSCh. 9.2 - Prob. 61PSCh. 9.3 - Prob. 1CQCh. 9.3 - Prob. 2CQCh. 9.3 - Prob. 3CQCh. 9.3 - Prob. 4CQCh. 9.3 - Prob. 5CQCh. 9.3 - Prob. 6CQCh. 9.3 - Prob. 7CQCh. 9.3 - Prob. 8CQCh. 9.3 - Prob. 9CQCh. 9.3 - Prob. 10CQCh. 9.3 - For Problems 16, match the function with its graph...Ch. 9.3 - For Problems 16, match the function with its graph...Ch. 9.3 - Prob. 3PSCh. 9.3 - Prob. 4PSCh. 9.3 - For Problems 16, match the function with its graph...Ch. 9.3 - Prob. 6PSCh. 9.3 - Prob. 7PSCh. 9.3 - Prob. 8PSCh. 9.3 - Prob. 9PSCh. 9.3 - Prob. 10PSCh. 9.3 - Prob. 11PSCh. 9.3 - Prob. 12PSCh. 9.3 - Prob. 13PSCh. 9.3 - Prob. 14PSCh. 9.3 - Prob. 15PSCh. 9.3 - Prob. 16PSCh. 9.3 - Prob. 17PSCh. 9.3 - Prob. 18PSCh. 9.3 - Prob. 19PSCh. 9.3 - Prob. 20PSCh. 9.3 - Prob. 21PSCh. 9.3 - Prob. 22PSCh. 9.3 - Prob. 23PSCh. 9.3 - Prob. 24PSCh. 9.3 - Prob. 25PSCh. 9.3 - Prob. 26PSCh. 9.3 - Prob. 27PSCh. 9.3 - Prob. 28PSCh. 9.3 - Prob. 29PSCh. 9.3 - Prob. 30PSCh. 9.3 - Prob. 31PSCh. 9.3 - Prob. 32PSCh. 9.3 - Prob. 33PSCh. 9.3 - Prob. 34PSCh. 9.3 - Prob. 35PSCh. 9.3 - Prob. 36PSCh. 9.3 - Prob. 37PSCh. 9.3 - Prob. 38PSCh. 9.3 - Prob. 39PSCh. 9.3 - Prob. 40PSCh. 9.3 - Prob. 41PSCh. 9.3 - Prob. 42PSCh. 9.3 - Prob. 43PSCh. 9.3 - Prob. 44PSCh. 9.3 - Prob. 45PSCh. 9.3 - Prob. 46PSCh. 9.3 - Prob. 47PSCh. 9.3 - Prob. 48PSCh. 9.3 - Prob. 49PSCh. 9.3 - Prob. 50PSCh. 9.3 - Prob. 51PSCh. 9.3 - Prob. 52PSCh. 9.3 - Prob. 53PSCh. 9.3 - Prob. 54PSCh. 9.3 - Prob. 55PSCh. 9.3 - Prob. 56PSCh. 9.3 - Prob. 57PSCh. 9.3 - Prob. 58PSCh. 9.3 - Prob. 59PSCh. 9.3 - Prob. 60PSCh. 9.3 - Prob. 61PSCh. 9.3 - Prob. 62.1PSCh. 9.3 - Prob. 62.2PSCh. 9.3 - Prob. 62.3PSCh. 9.3 - Use the definition of absolute value to help you...Ch. 9.3 - Prob. 62.5PSCh. 9.3 - Prob. 63PSCh. 9.3 - Prob. 64PSCh. 9.3 - Prob. 65PSCh. 9.3 - Prob. 66PSCh. 9.3 - Prob. 67PSCh. 9.3 - Prob. 68.1PSCh. 9.3 - Prob. 68.2PSCh. 9.3 - Prob. 68.3PSCh. 9.3 - Prob. 68.4PSCh. 9.3 - Prob. 68.5PSCh. 9.3 - Prob. 68.6PSCh. 9.3 - Prob. 68.7PSCh. 9.3 - For each of the following, answer the question on...Ch. 9.3 - Prob. 68.9PSCh. 9.3 - Prob. 69PSCh. 9.3 - Prob. 70PSCh. 9.4 - Prob. 1CQCh. 9.4 - Prob. 2CQCh. 9.4 - Prob. 3CQCh. 9.4 - Prob. 4CQCh. 9.4 - Prob. 5CQCh. 9.4 - Prob. 6CQCh. 9.4 - Prob. 7CQCh. 9.4 - Prob. 8CQCh. 9.4 - Prob. 9CQCh. 9.4 - Prob. 10CQCh. 9.4 - Prob. 1PSCh. 9.4 - For Problems 118, determine (fg)(x).and (gf)(x)...Ch. 9.4 - Prob. 3PSCh. 9.4 - Prob. 4PSCh. 9.4 - Prob. 5PSCh. 9.4 - Prob. 6PSCh. 9.4 - Prob. 7PSCh. 9.4 - Prob. 8PSCh. 9.4 - Prob. 9PSCh. 9.4 - Prob. 10PSCh. 9.4 - Prob. 11PSCh. 9.4 - Prob. 12PSCh. 9.4 - Prob. 13PSCh. 9.4 - For Problems 118, determine (fg)(x).and (gf)(x)...Ch. 9.4 - Prob. 15PSCh. 9.4 - Prob. 16PSCh. 9.4 - Prob. 17PSCh. 9.4 - Prob. 18PSCh. 9.4 - Prob. 19PSCh. 9.4 - Prob. 20PSCh. 9.4 - Prob. 21PSCh. 9.4 - For Problems 1926, show that (fg)(x)=x and...Ch. 9.4 - Prob. 23PSCh. 9.4 - Prob. 24PSCh. 9.4 - Prob. 25PSCh. 9.4 - Prob. 26PSCh. 9.4 - Prob. 27PSCh. 9.4 - Prob. 28PSCh. 9.4 - Prob. 29PSCh. 9.4 - Prob. 30PSCh. 9.4 - Prob. 31PSCh. 9.4 - Prob. 32PSCh. 9.4 - Prob. 33PSCh. 9.4 - Prob. 34PSCh. 9.4 - Prob. 35PSCh. 9.4 - Prob. 36PSCh. 9.4 - Prob. 37PSCh. 9.4 - Prob. 38PSCh. 9.4 - Prob. 39.1PSCh. 9.4 - Prob. 39.2PSCh. 9.4 - Prob. 39.3PSCh. 9.4 - Prob. 39.4PSCh. 9.4 - Prob. 39.5PSCh. 9.5 - Prob. 1CQCh. 9.5 - Prob. 2CQCh. 9.5 - Prob. 3CQCh. 9.5 - Prob. 4CQCh. 9.5 - Prob. 5CQCh. 9.5 - Prob. 6CQCh. 9.5 - Prob. 7CQCh. 9.5 - Prob. 8CQCh. 9.5 - Prob. 9CQCh. 9.5 - Prob. 10CQCh. 9.5 - Prob. 1PSCh. 9.5 - Prob. 2PSCh. 9.5 - Prob. 3PSCh. 9.5 - Prob. 4PSCh. 9.5 - Prob. 5PSCh. 9.5 - Prob. 6PSCh. 9.5 - Prob. 7PSCh. 9.5 - Prob. 8PSCh. 9.5 - Prob. 9PSCh. 9.5 - Prob. 10PSCh. 9.5 - Prob. 11PSCh. 9.5 - Prob. 12PSCh. 9.5 - Prob. 13PSCh. 9.5 - Prob. 14PSCh. 9.5 - Prob. 15PSCh. 9.5 - Prob. 16PSCh. 9.5 - Prob. 17PSCh. 9.5 - Prob. 18PSCh. 9.5 - Prob. 19PSCh. 9.5 - Prob. 20PSCh. 9.5 - Prob. 21PSCh. 9.5 - Prob. 22PSCh. 9.5 - Prob. 23PSCh. 9.5 - Prob. 24PSCh. 9.5 - Prob. 25PSCh. 9.5 - Prob. 26PSCh. 9.5 - Prob. 27PSCh. 9.5 - Prob. 28PSCh. 9.5 - Prob. 29PSCh. 9.5 - Prob. 30PSCh. 9.5 - Prob. 31PSCh. 9.5 - Prob. 32PSCh. 9.5 - Prob. 33PSCh. 9.5 - Prob. 34PSCh. 9.5 - Prob. 35PSCh. 9.5 - Prob. 36PSCh. 9.5 - Prob. 37PSCh. 9.5 - Prob. 38PSCh. 9.5 - Prob. 39PSCh. 9.5 - Prob. 40PSCh. 9.5 - Prob. 41PSCh. 9.5 - Prob. 42PSCh. 9.5 - Prob. 43PSCh. 9.5 - Prob. 44PSCh. 9.5 - Prob. 45PSCh. 9.5 - Prob. 46PSCh. 9.5 - Prob. 47PSCh. 9.5 - Prob. 48PSCh. 9.5 - Prob. 49PSCh. 9.5 - Prob. 50PSCh. 9.5 - Prob. 51PSCh. 9.5 - Prob. 52PSCh. 9.5 - Prob. 53PSCh. 9.5 - Prob. 54PSCh. 9.5 - Prob. 55PSCh. 9.5 - Prob. 56PSCh. 9.6 - Prob. 1CQCh. 9.6 - Prob. 2CQCh. 9.6 - Prob. 3CQCh. 9.6 - Prob. 4CQCh. 9.6 - Prob. 5CQCh. 9.6 - Prob. 6CQCh. 9.6 - Prob. 7CQCh. 9.6 - Prob. 8CQCh. 9.6 - Prob. 9CQCh. 9.6 - Prob. 10CQCh. 9.6 - Prob. 1PSCh. 9.6 - Prob. 2PSCh. 9.6 - Prob. 3PSCh. 9.6 - Prob. 4PSCh. 9.6 - Prob. 5PSCh. 9.6 - For Problems 110, translate each statement of...Ch. 9.6 - Prob. 7PSCh. 9.6 - Prob. 8PSCh. 9.6 - For Problems 110, translate each statement of...Ch. 9.6 - For Problems 110, translate each statement of...Ch. 9.6 - Prob. 11PSCh. 9.6 - Prob. 12PSCh. 9.6 - Prob. 13PSCh. 9.6 - Prob. 14PSCh. 9.6 - Prob. 15PSCh. 9.6 - Prob. 16PSCh. 9.6 - Prob. 17PSCh. 9.6 - Prob. 18PSCh. 9.6 - Prob. 19PSCh. 9.6 - Prob. 20PSCh. 9.6 - Prob. 21PSCh. 9.6 - Prob. 22PSCh. 9.6 - Prob. 23PSCh. 9.6 - Prob. 24PSCh. 9.6 - Prob. 25PSCh. 9.6 - Prob. 26PSCh. 9.6 - Prob. 27PSCh. 9.6 - Prob. 28PSCh. 9.6 - Prob. 29PSCh. 9.6 - Prob. 30PSCh. 9.6 - Prob. 31PSCh. 9.6 - Prob. 32PSCh. 9.6 - Prob. 33PSCh. 9.6 - Prob. 34PSCh. 9.6 - Prob. 35PSCh. 9.6 - Prob. 36PSCh. 9.6 - Solve each of the following problems. Objective...Ch. 9.6 - Prob. 38PSCh. 9.6 - Prob. 39PSCh. 9.6 - Prob. 40PSCh. 9.6 - Prob. 41PSCh. 9.6 - Prob. 42PSCh. 9.6 - Prob. 43PSCh. 9.6 - Prob. 44PSCh. 9.6 - Prob. 45PSCh. 9.6 - Prob. 46PSCh. 9.S - Specify the domain and range of the relation and...Ch. 9.S - Prob. 2SCh. 9.S - Prob. 3SCh. 9.S - Prob. 4SCh. 9.S - Prob. 5SCh. 9.S - Prob. 6SCh. 9.S - Prob. 7SCh. 9.S - Suppose the cost function for producing a...Ch. 9.S - Graph f(x)=|x3|+1.Ch. 9.S - Prob. 10SCh. 9.S - Prob. 11SCh. 9.S - Prob. 12SCh. 9.S - Prob. 13SCh. 9.S - Prob. 14SCh. 9.S - Prob. 15SCh. 9.S - Prob. 16SCh. 9.S - Prob. 17SCh. 9.S - Prob. 18SCh. 9.S - Prob. 19SCh. 9.S - Prob. 20SCh. 9.S - Prob. 21SCh. 9.CR - For Problems 14, determine if the following...Ch. 9.CR - Prob. 2CRCh. 9.CR - Prob. 3CRCh. 9.CR - Prob. 4CRCh. 9.CR - Prob. 5CRCh. 9.CR - Prob. 6CRCh. 9.CR - Prob. 7CRCh. 9.CR - Prob. 8CRCh. 9.CR - Prob. 9CRCh. 9.CR - For Problems 710, specify the domain of each...Ch. 9.CR - Prob. 11CRCh. 9.CR - Prob. 12CRCh. 9.CR - Prob. 13CRCh. 9.CR - Prob. 14CRCh. 9.CR - For Problems 1522, graph each of the functions....Ch. 9.CR - For Problems 1522, graph each of the functions....Ch. 9.CR - Prob. 17CRCh. 9.CR - Prob. 18CRCh. 9.CR - Prob. 19CRCh. 9.CR - Prob. 20CRCh. 9.CR - Prob. 21CRCh. 9.CR - Prob. 22CRCh. 9.CR - Prob. 23CRCh. 9.CR - An outpatient operating room charges each patient...Ch. 9.CR - Prob. 25CRCh. 9.CR - Prob. 26CRCh. 9.CR - Prob. 27CRCh. 9.CR - Prob. 28CRCh. 9.CR - Prob. 29CRCh. 9.CR - Prob. 30CRCh. 9.CR - Prob. 31CRCh. 9.CR - Prob. 32CRCh. 9.CR - Prob. 33CRCh. 9.CR - Find the coordinates of the vertex and the...Ch. 9.CR - Find two numbers whose sum is 40 and whose product...Ch. 9.CR - Prob. 36CRCh. 9.CR - A garden has 60 yards of fencing and wants to...Ch. 9.CR - Suppose that 50 students are able to raise 250 for...Ch. 9.CR - Prob. 39CRCh. 9.CR - Prob. 40CRCh. 9.CR - Prob. 41CRCh. 9.CR - Prob. 42CRCh. 9.CR - Prob. 43CRCh. 9.CR - Prob. 44CRCh. 9.CR - Prob. 45CRCh. 9.CR - Prob. 46CRCh. 9.CR - Prob. 47CRCh. 9.CR - Prob. 48CRCh. 9.CR - For Problems 3956, graph the functions. f(x)=|x2|Ch. 9.CR - Prob. 50CRCh. 9.CR - Prob. 51CRCh. 9.CR - Prob. 52CRCh. 9.CR - Prob. 53CRCh. 9.CR - Prob. 54CRCh. 9.CR - Prob. 55CRCh. 9.CR - Prob. 56CRCh. 9.CR - Prob. 57CRCh. 9.CR - Prob. 58CRCh. 9.CR - Prob. 59CRCh. 9.CR - Prob. 60CRCh. 9.CR - Prob. 61CRCh. 9.CR - Prob. 62CRCh. 9.CR - Prob. 63CRCh. 9.CR - Prob. 64CRCh. 9.CR - Prob. 65CRCh. 9.CR - Prob. 66CRCh. 9.CR - Prob. 67CRCh. 9.CR - Prob. 68CRCh. 9.CR - Prob. 69CRCh. 9.CR - Prob. 70CRCh. 9.CR - Prob. 71CRCh. 9.CR - Prob. 72CRCh. 9.CR - Prob. 73CRCh. 9.CR - The surface area of a cube varies directly as the...Ch. 9.CR - Prob. 75CRCh. 9.CR - Prob. 76CRCh. 9.CR - Prob. 77CRCh. 9.CR - Prob. 78CRCh. 9.CT - Prob. 1CTCh. 9.CT - Prob. 2CTCh. 9.CT - Prob. 3CTCh. 9.CT - Prob. 4CTCh. 9.CT - Prob. 5CTCh. 9.CT - Prob. 6CTCh. 9.CT - Prob. 7CTCh. 9.CT - Prob. 8CTCh. 9.CT - Prob. 9CTCh. 9.CT - Prob. 10CTCh. 9.CT - Prob. 11CTCh. 9.CT - Prob. 12CTCh. 9.CT - Prob. 13CTCh. 9.CT - Prob. 14CTCh. 9.CT - Prob. 15CTCh. 9.CT - Prob. 16CTCh. 9.CT - Prob. 17CTCh. 9.CT - Prob. 18CTCh. 9.CT - Prob. 19CTCh. 9.CT - Prob. 20CTCh. 9.CT - Prob. 21CTCh. 9.CT - Prob. 22CTCh. 9.CT - Prob. 23CTCh. 9.CT - Prob. 24CTCh. 9.CT - Prob. 25CT
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Author:Carter
Publisher:McGraw Hill
Implicit Differentiation with Transcendental Functions; Author: Mathispower4u;https://www.youtube.com/watch?v=16WoO59R88w;License: Standard YouTube License, CC-BY
How to determine the difference between an algebraic and transcendental expression; Author: Study Force;https://www.youtube.com/watch?v=xRht10w7ZOE;License: Standard YouTube License, CC-BY