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Ⓡ=-3ex+3 0-3√4-x= 04-z = 04 = xx = 4(-1) 0#(-4)-3 (-1)0x0=(1)e#!(1)44Positive: (-∞, -3)Negative: (-3,0) U (0,4)2Next we determine all placeswithin the domain of f(x) thatf(x)= 0. This happens when-ever the top of the fraction isequal to zero, and to solve thatequation, we set each individualfactor equal to zero and solvethose equations. Note that eachof the solutions is in the domainof f(x), so f(x) has zeros atx = -3 and x = 4.The zero z 4 is already plot-ted on the number line since itis the edge of the domain, so weadd the other zero x = -3 to thenumber line.Next we choose a test value ineach interval to help us deter-mine the sign of each interval.We indicate these test values inparentheses since they are notuniquely chosen.First note that the factor√4x and the factor ² areboth positive on every interval,so it remains to determine thesign of the factor a +3 and thefactor - - 5 for each interval.staat mal.For the test value -4, the factorx + 3 is negative and the factorx-5 is negative. That givesus a positive value overall forthat interval. For the test value-1, the factor x + 3 is positive.and the factor - 5 is negative.That gives us a negative valueoverall for that interval. For thetest value 1, the factor x + 3 ispositive and the factor - 5is negative. That gives us anegative value overall for thatinterval.With the sign of each intervaldetermined, we can now use in-terval notation to provide the in-tervals on which f(x) is positiveand on which f(x) is negative. Show What You Know: Solving Inequalities withVarious Function TypesMAT 190 PrecalculusObjectives: 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 onwhich the function is negative:x - 3ex (x - 5)² √2x + 1f(x)Include a detailed explanation for each mathematical step written in grammatically correctcomplete sentences within a 2-column format.Sample Problem and Solution:Problem: Find all intervals on which the following function is positive and all intervals onwhich the following function is negative:

Answered: Image /qna-images/answer/93ef2bba-75eb-4e85-8ccb-3438c0dc4d0e.jpg

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

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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Question

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.

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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