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Find all intervals on which the function is positive and all intervals on which the function is negative: Assignment: f(x) = x-3 ex (x - 5)² √2x +1° Include a detailed explanation for each mathematical step written in grammatically correct complete sentences within a 2-column format.

Find all intervals on which the function is positive and all intervals on which the function is negative: Assignment: f(x) = x-3 ex (x - 5)² √2x +1° Include a detailed explanation for each mathematical step written in grammatically correct complete sentences within a 2-column format.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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help solve this problem please. find positives and negatives. factor it & plot the domain. An example will be provided in the second photo
(x+3)√4 x = 0 Ⓡ = -3 e x+3 0 -3 √4-x = 0 4-z = 0 4 = x x = 4 (-1) 0 # (-4)-3 (-1) 0 x 0 = (1) e #! (1) 4 4 Positive: (-∞, -3) Negative: (-3,0) U (0,4) 2 Next we determine all places within the domain of f(x) that f(x)= 0. This happens when- ever the top of the fraction is equal to zero, and to solve that equation, we set each individual factor equal to zero and solve those equations. Note that each of the solutions is in the domain of f(x), so f(x) has zeros at x = -3 and x = 4. The zero z 4 is already plot- ted on the number line since it is the edge of the domain, so we add the other zero x = -3 to the number line. Next we choose a test value in each interval to help us deter- mine the sign of each interval. We indicate these test values in parentheses since they are not uniquely chosen. First note that the factor √4x and the factor ² are both positive on every interval, so it remains to determine the sign of the factor a +3 and the factor - - 5 for each interval. staat mal. For the test value -4, the factor x + 3 is negative and the factor x-5 is negative. That gives us a positive value overall for that interval. For the test value -1, the factor x + 3 is positive. and the factor - 5 is negative. That gives us a negative value overall for that interval. For the test value 1, the factor x + 3 is positive and the factor - 5 is negative. That gives us a negative value overall for that interval. With the sign of each interval determined, we can now use in- terval notation to provide the in- tervals on which f(x) is positive and on which f(x) is negative.
Transcribed Image Text:(x+3)√4 x = 0 Ⓡ = -3 e x+3 0 -3 √4-x = 0 4-z = 0 4 = x x = 4 (-1) 0 # (-4)-3 (-1) 0 x 0 = (1) e #! (1) 4 4 Positive: (-∞, -3) Negative: (-3,0) U (0,4) 2 Next we determine all places within the domain of f(x) that f(x)= 0. This happens when- ever the top of the fraction is equal to zero, and to solve that equation, we set each individual factor equal to zero and solve those equations. Note that each of the solutions is in the domain of f(x), so f(x) has zeros at x = -3 and x = 4. The zero z 4 is already plot- ted on the number line since it is the edge of the domain, so we add the other zero x = -3 to the number line. Next we choose a test value in each interval to help us deter- mine the sign of each interval. We indicate these test values in parentheses since they are not uniquely chosen. First note that the factor √4x and the factor ² are both positive on every interval, so it remains to determine the sign of the factor a +3 and the factor - - 5 for each interval. staat mal. For the test value -4, the factor x + 3 is negative and the factor x-5 is negative. That gives us a positive value overall for that interval. For the test value -1, the factor x + 3 is positive. and the factor - 5 is negative. That gives us a negative value overall for that interval. For the test value 1, the factor x + 3 is positive and the factor - 5 is negative. That gives us a negative value overall for that interval. With the sign of each interval determined, we can now use in- terval notation to provide the in- tervals on which f(x) is positive and on which f(x) is negative.
Show What You Know: Solving Inequalities with Various Function Types MAT 190 Precalculus Objectives: The purpose of this assignment is for you to: 1. demonstrate your ability to solve inequalities with various function types; 2. improve your mathematical writing to include full solutions with justifications; 3. integrate mathematical statements into grammatically correct expositions. Assignment: Find all intervals on which the function is positive and all intervals on which the function is negative: x - 3 ex (x - 5)² √2x + 1 f(x) Include a detailed explanation for each mathematical step written in grammatically correct complete sentences within a 2-column format. Sample Problem and Solution: Problem: Find all intervals on which the following function is positive and all intervals on which the following function is negative:
Transcribed Image Text:Show What You Know: Solving Inequalities with Various Function Types MAT 190 Precalculus Objectives: The purpose of this assignment is for you to: 1. demonstrate your ability to solve inequalities with various function types; 2. improve your mathematical writing to include full solutions with justifications; 3. integrate mathematical statements into grammatically correct expositions. Assignment: Find all intervals on which the function is positive and all intervals on which the function is negative: x - 3 ex (x - 5)² √2x + 1 f(x) Include a detailed explanation for each mathematical step written in grammatically correct complete sentences within a 2-column format. Sample Problem and Solution: Problem: Find all intervals on which the following function is positive and all intervals on which the following function is negative:
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