# Algebra : Graphing Functions

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Can you please assist me with the problems listed below?

P. 237

1. a) #6, b) #18

2. a) #22, b) #24

3. a) #32, b) #46

P.253

4. a) #1, b) #2, c) #3. d_ #4

5. a) #10, b) #12

6. a) # 28, b) #30

7. P.260, Matched Problem 1

P.271

8. # 2 - 22 (Even #s)

9 a) # 24, b) #36

10. a) #50, b) #78

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##### Solution Summary

Many questions related to the graphing of functions are answered in detail. Graph drawings are included. Questions relate to domains, ranges, extrema, vertices, axes and one-to-one functions.

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P237

A

6. Domain

Range

X intercepts: None

Y intercepts: 2

Interval over which f is increasing :

Interval over which f is decreasing: None

Interval over which f is constant: [-3,3]

Discontinuity: x= -3.

Note: Since I don't know which points ( (-3,-2) or (-3,2) ) are closed or open.

If (-3,2) is closed, then the interval over which f is constant is [-3,3];

If (-3,2) is open, then the interval over which f is constant is (-3,3];

B.

18.

22.

The axis: x=2

Vertex: (2,4)

Maximum: f(x)=4

No minimum

Range:

24.

The axis: x=3

Vertex: (3,-4)

No Maximum

Minimum: -4

Range:

...

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

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- "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."
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