Answers
You may be asked to "determine algebraically" whether a function is even or odd. To do this, you take the function and plug –x in for x, and then simplify. If you end up with the exact same function that you started with (that is, if f (–x) = f (x), so all of the signs are the same), then the function is even. If you end up with the exact opposite of what you started with (that is, if f (–x) = –f (x), so all of the signs are switched), then the function is odd.
In all other cases, the function is "neither even nor odd".
Let's see what this looks like in action:
Determine algebraically whether f (x) = –3x2 + 4 is even, odd, or neither.
If I graph this, I will see that this is "symmetric about the y-axis"; in other words, whatever the graph is doing on one side of the y-axis is mirrored on the other side:
graph of y = –3x^2 + 4
This mirroring about the y-axis is a hallmark of even functions.
Also, I note that the exponents on all of the terms are even — the exponent on the constant term being zero: 4x0 = 4 × 1 = 4. These are helpful clues that strongly suggest to me that I've got an even function here.
But the question asks me to make the determination algebraically, which means that I need to do the algebra.
So I'll plug –x in for x, and simplify:
f (–x) = –3(–x)2 + 4
= –3(x2) + 4
= –3x2 + 4
I can see, by comparing the original function with my final result above, that I've got a match, which means that:
f (x) is even
Related Questions
A cell phone company charges $25 per month, plus $0.10 per text message sent. Before taxes, Susie’s bill was $80 for 3 months of service. How many text messages did Susie send during those 3
Answers
let m = the number of months
let t = each message sent
25m + 0.1t = 80
plug 3 in for m (because 3 months)
25(3) + 0.1t = 80
simplify
75 + 0.1t = 80
subtract 75 from 80
0.1t = 5
divide 5 by 0.1
t = 50
answer: 50 text messages
A study is performed in a large southern town to determine whether the average amount spent on food per four-person family in the town is significantly different from the national average. A random sample of the weekly grocery bills of two-person families in this town is given in the file. Assume the national average amount spent on food for a four-person family is $150.
a. Identify the null and alternative hypotheses for this situation.
b. Is the sample evidence statistically significant? If so, at what significance levels can you reject the null hypothesis?
c. For which values of the sample mean (e.g., average weekly grocery bill) would you reject the null hypothesis at the 1% significance level? For which values of the sample mean would you reject the null hypothesis at the 10% level?
Family Weekly food expense
1 $198.23
2 $143.53
3 $207.48
4 $134.55
5 $182.01
6 $189.84
7 $170.36
8 $163.72
9 $155.73
10 $203.73
11 $191.19
12 $172.66
13 $154.25
14 $179.03
15 $130.29
16 $170.73
17 $194.50
18 $171.14
19 $175.19
20 $177.25
21 $166.62
22 $135.54
23 $141.18
24 $158.48
25 $159.78
26 $157.42
27 $98.40
28 $181.63
29 $128.45
30 $190.84
31 $154.04
32 $190.22
33 $161.48
34 $113.42
35 $148.83
36 $197.68
37 $135.49
38 $146.72
39 $176.62
40 $154.60
41 $178.39
42 $186.32
43 $157.94
44 $116.35
45 $136.81
46 $195.58
47 $129.44
48 $146.84
49 $165.63
50 $158.97
51 $210.00
52 $175.46
53 $159.69
54 $154.56
55 $152.95
56 $177.30
57 $129.23
58 $127.40
59 $167.48
60 $183.83
61 $157.39
62 $163.24
63 $165.01
64 $137.43
65 $177.37
66 $142.68
67 $150.04
68 $161.44
69 $166.13
70 $190.96
71 $187.19
72 $116.63
73 $159.73
74 $159.64
75 $142.44
76 $153.03
77 $143.12
78 $156.35
79 $182.70
80 $129.03
81 $119.06
82 $137.99
83 $144.20
84 $183.51
85 $169.67
86 $134.66
87 $202.94
88 $143.43
89 $170.52
90 $139.53
91 $159.31
92 $134.77
93 $165.48
94 $127.20
95 $168.16
96 $125.39
97 $167.96
98 $178.64
99 $134.38
100 $111.87
Answers
Step-by-step explanation:
H0: u = 150
H1: u ≠ 150
Total sum = 15933.24
N = 100
Mean = 15933.24/100
= 159.3324
σ² = 25954.03 - (159.3324)²/100
σ² = 556.213
σ = √556.213
σ = 23.8162
Testing hypothesis
t = (bar x - u)/ σ/√n
= 159.3324-150/23.8162/√100
= 3.91
We will have a p value of 0.02
0.0002 < 0.01
We reject null hypothesis at 1% level of significance
C. Mean = 159.3324
Se= 2.3936
Df = 100-1 = 99
Critical value at 0.01 = +-2.626
T = x-u/s.e
= -2.626 =( x -150)/2.3936
When we cross multiply and solve this
X = 143.714 for the lower tail
2.626 = (x-159)/2.3936
= 156.286 for upper tail.
We therefore reject H0 at
Bar X <= 143.71
Bar X >= 156.286
At 10%
Critical t = 1.660
-1.660 = (x - 150)/2.3936
Solving this ,
X =146.02 at the lower tail
1.660 = (x-150)/2.3936
X = 153.97
We reject H0 at
X<= 146.03
X>=153.97
12x ÷ 4y (if x = -8 and y = 3)
Answers
Answer: -8
Step-by-step explanation:
Find all the factors of 125
Answers
Answer:
1,5,25,125,
all can be added or multiplied to equal 125
Henry wants to earn at least $41 trimming trees. He charges $8 per hour and pays $7 in equipment fees. What are the possible numbers of hours Henry could trim trees?
Use t for the number of hours.
Write your answer as an inequality solved for t.
Answers
Answer:
8t - 7 ≤ 41 || t ≤ 6
Step-by-step explanation:
8t - 7 ≤ 41
+7 +7
---------------
8t ≤ 48
÷8 ÷8
----------------
t ≤ 6
Please help and the answer be right thanks
Answers
Step-by-step explanation: Tip you should down load an app called Photomath. You take a picture of your math problem and it tells you the answer tells you the steps on how to do it. It only works for math number problems only not word problems. I hope this helps :)
What is the value of X? x +31 equals 66
Answers
Answer:
35
Step-by-step explanation:
Simply subtract 31 from 66 to receive the value of x
Answer:
X = 35
Step-by-step explanation:
Take 31 over to the other side so the equation looks like this
[tex]x = 66 - 31[/tex]
Then, solve for 66 - 31.
You will end up with x = 35.
You can also check your work by substituting X with 35.
Hopefully this helped :)
I Given f(x) = 3x + 2 and g(x)= x? – 5. Find each of the following functions.
1. (f+g)(x)
2. (f- g)(x)
3. (fg)(x)
4. (f/g)(x)
2
Answers
Answer:
a) 4x-3
b)2x+7
c) 3x^2-13x-10
d) (3x^2+2)/(x-5)
Step-by-step explanation:
If you care to learn how these were solved and weren't just looking for answer let me know.
2 books cost 60 dollars how much will it cost for 5 books
Answers
Answer:
150 $
Step-by-step explanation:
60 :2 =30$cost a book
5×30 =150 $cost 5 books
Or
2 books..... 60 $
5 books...... x$
x=60 ×5 :2
x=300 :2
x=150$
Answer:
60 divided by 2 is 30 meaning 30$ for each book times 5 = 150 $
Step-by-step explanation:
hope i helped
Perform the indicated operations. Express the result in scientific notation.
(5.7 x 105) + (4.6 x 106)-(2.9 x 105)
O 7.4 x 105
O 3.3 x 106
O 4.88 x 106
O 5.17 x 106
Answers
Answer:
The answer is C 4.88 x 106
Step-by-step explanation:
=2 2/5 x 4 (What is the answer?)
Answers
Answer:
um 22 /20
is the question
if it's the case of factorised
than answer is 11/10
Answer:
48/5
Step-by-step explanation:
I will assume that you mean [tex](2\frac{2}{5}) \cdot 4[/tex].
This is equivalent to [tex](\frac{12}{5}) \cdot 4 = \boxed{\frac{48}{5}}[/tex]
Write the equation for the vertical line going through the point (16,25).
Answers
Answer:
x=16
Step-by-step explanation:
Vertical lines are of the form
x=
Since the x coordinate is 16
x=16
Answer: 16
Step-by-step explanation: x is on 16
If the slope of a line is -1 and two points on the line are (-9, 3) and (-10, r), what is the value of r?
Answers
Answer:
[tex]r=4[/tex]
Step-by-step explanation:
We know that the slope of the line is -1.
We also know that the line passes through (-9, 3) and (-10, r).
We want to find the value of r.
First, let's figure out the equation of our line. We can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and (x₁, y₁) is a point.
So, let's substitute -1 for m. Since we know the point (-9, 3), let's use this for (x₁, y₁).
Substitute:
[tex]y-(3)=-1(x-(-9))[/tex]
Simplify:
[tex]y-3=-(x+9)[/tex]
Distribute:
[tex]y-3=-x-9[/tex]
Add 3 to both sides. So, our equation is:
[tex]y=-x-6[/tex]
It passes through (-10, r) and we want to find the value of r. So, let's substitute -10 for x and r for y, since -10 is our x and r is our y. So:
[tex]r=-(-10)-6[/tex]
Evaluate for r. Distribute:
[tex]r=10-6[/tex]
Subtract:
[tex]r=4[/tex]
So, the value of r is 4.
And we're done!
what is 8.42 times 10 to the 3rd power
Answers
Answer:
8420
Step-by-step explanation:
10 to the third power will move the decimal point three place values to the right. So, the first two times you move it, you get 842, and so there is a 0 on the end to signify that it moved the third time.
Find the maturity value and the compound interest if $3,600 is invested at 6% compounded semi-
annually for 5 years and 7 months. Round your final answers to 2 decimal places
Answers
Answer:Answer Expert Verified. The Answer is that the present value of $100 is $100. Because this $100 dollar is deposited today so the time is equal to zero and when time is zero the value of amount is the value of amount itself.
Step-by-step explanation:
a charity raised about 8200. if the amount of money was rounded to the nearest hundred dollars, what ciuld have been the exact amount?
Answers
Answer:
Anything from 8150 to 8249
please help quickly!!!! i only have 5 minutes left ill give brainliest
Answers
Answer:
y=1/3x+2
Step-by-step explanation:
To solve, you plug in each vaule for x and y in the table. If it is a true statement for more than 1 answer, thats the correct answer
Answer: C
Step-by-step explanation:
I had this question before
What is the midpoint between the following two points
(3,-2) & (9,2)
A) (6,0)
B) (0,6)
C) (3,1)
D) (3,2)
Answers
Answer:
B, (6,0)
Take the average of the x values and the average of the y values:
(3+9)/2 = 6
(-2+2)/2 = 0
This means the answer (the average (midpoint) of the two points) is (6,0)
(WILL MARK BRAINLIEST!)
What is 0.08 written as a fraction in simplest form?
A. 1/125
B. 2/25
C. 1/12
D. 4/5
Answers
Answer:
B. 2/25
Step-by-step explanation:
Answer:
Step-by-step explanation:
B. 2/25
I dont understand do I multiply four to get the area?
Answers
Answer:
yes
Step-by-step explanation:
3×5×45=365m²
Answer:
yes
Step-by-step explanation:
Simplify the expression.
(x4y2)1/2
A) 2(x4y2)
B) x1/8y1/4
C) x2y
D) x8y4
Answers
Answer:
C)
when you distrbe you get x^2 y
Stanley is looking to retire and move near the ocean. The Jersey Shore has seen a rise in sea levels the past few years. These high tides have caused floods in 100 places that call themselves Jersey Shore towns, which are on or within reasonable distance of the ocean. Stanley is nervous about possible floods and would like to be prepared for costs associated with them. As Stanley’s friend and an expert in risk management, you collect past information and have constructed the following probability distribution for the number of floods per town per summer at the Jersey Shore. # of floods per town per summer Probability 0 0.10 1 0.15 2 0.26 3 0.30 4 0.15 5 0.04 a. Calculate the expected frequency of floods per town per summer. (2 points) b. Calculated the variance. (2 points)
Answers
Answer:
2.37 ; 1.6731
Step-by-step explanation:
Given the data:
X:___0____1____2____3____4____5
P(x):_0.10_0.15_0.26__0.30_0.15__0.04
the expected frequency of floods per town per summer
Σ(flood per Town per summer) * probability
Σ(X)*p(x)
Σ(0*0.10) + (1*0.15) + (2*0.26) + (3*0.30) + (4*0.15) + (5*0.04)
= (0 + 0.15 + 0.52 + 0.90 + 0.60 + 0.2)
= 2.37
Variance (s²) :
Σ[x². P(x)] - u²
Using an online variance calculator to save computation time :
s² = 16731 / 10000
s² = 1.6731
A restaurant uses 4 pounds of potatoes for a party of 12 people if they are cooking potatoes for a party of 60 people,what should they do?
Answers
Answer:
They should multiply the amount of potatoes by 5. 12 is 1/5 of 60. Therefore, if you need 4 pounds of potatoes for 12 people, then you will need 20 pounds of potatoes for 60 people.
Step-by-step explanation:
The scale of a map is 6 km = 4 mi. What is the length on the map if the actual is 40.1
miles.
Answers
Answer:
60.15 km
Step-by-step explanation:
If 6 km on the map represents 4 mi on land, then we'd get the answer by using the relation
6 km -> 4 mi
x km -> 40.1 mi
Where x km is the length on the map we're looking for. If we cross multiply
6 * 40.1 = 4x
240.6 = 4x
x = 240.6/4
x = 60.15 km.
That is the length we're looking for
18% of 200 is between which two numbers?
Answers
Answer:
35&37
Step-by-step explanation:
Well 18% of 200 is 36 so...
If a =3.6 and b=10 then ab=
Answers
Answer:
36
Step-by-step explanation:
ab = a*b
a=3.6
b=10
3.6*10
=36
7 is 10 times the value of what number
Answers
Answer:
0.7
Step-by-step explanation:
7/10=0.7
11/12 of the disk space on a
hard drive is unused. 3 people
need to use the remaining disk
space evenly. How much of the
total disk space will 1 user get?
Answers
Answer:
2 whole number 1 out of 4
Step-by-step explanation:
11/12 x 3
11/4 = 2remainder 3
2 whole number 3 out of 12
When u reduce it will be 2 whole number 1 out of 4
What is the value of the expression below when x=8? 10x+5
Answers
The equation will be 10(8)+5
2. Solve multiplication
80+5
3. The answer is 85! Hope this helped <3
What is the answer for 2
Answers
Answer:
C
Step-by-step explanation:
73.89 x .05 = 3.6945
but to round it will become 3.69
Answer:
C. $3.69
Step-by-step explanation:
73.89 × 0.05 = $3.6945$3.6945 rounds to $3.69I hope this helps!