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Graphs and Functions : Asymptotes, X- and Y-Intercepts, Inverses, One-to-one and pH and H+ Ion Concentration

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1. graph f(x) =
+ 5x+ 4
be sure to label all the asymptotes and to list the domain the x and y- intercept
2. f(x) = +3, x
- sketch the graph and use the graph to determine whether the function is one to one
-if the function is one to one find a formula the inverse
3. In chemistry the pH of the substance defined as
pH = -log [H ],
find the pH of each of the substance

substance hydrogen ion concentration
a) juice 1.6x 10
b) hire rinse 0.0013
c) mouthwash 6.3 x 10
d) eggs 1.6 x 10
e) tomatoes 6.3 x 10
4. solve using any method
ln(ln x) = 2
---

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Graphs and Functions, Asymptotes, X- and Y-Intercepts, Inverses, One-to-one and pH and H+ Ion Concentration are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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1. graph f(x) =
+ 5x+ 4
be sure to label all the asymptotes and to list the domain the x and y- intercept

Use Maple, we get the following graph:

The horizontal asymptote is y=0

Two vertical asymptotes are x=-1 and x=-4

x-intercept is ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
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