Study the function below and then answer the questions that follow. Equation What is the domain of f(x)? What is the range of f(x)?
Answers
Answer:
(a) Domain: All real numbers except -2
(b) [tex]f(x) > -4[/tex]
Step-by-step explanation:
Given
See attachment for f(x)
Solving (a): The domain
From the attached image, we have:
[tex]f(x) = -x - 2, x <-2[/tex]
[tex]f(x) = -x^2, -2 < x < 0[/tex]
[tex]f(x) = x, x \ge 0[/tex]
To get the domain, we consider the inequalities attached to each of the piece-wise function
[tex]x < -2[/tex]
This implies that the values of x is less than -2 i.e.
[tex]x = \{.......,-4,-3\}[/tex]
[tex]-2< x<0[/tex]
This implies that x is greater than -2 and less than 0 i.e.
[tex]x = \{-1\}[/tex]
[tex]x \ge 0[/tex]
This implies that x is greater than or equal to 0 i.e.
[tex]x =\{0,1,2,3,....\}[/tex]
If these values of x are merged, we have:
[tex]x = \{.......,-4,-3,-1,0,1,2,3.....\}[/tex]
[tex]x = \{-\infty,..,-4,-3,-1,0,1,2,3,...,\infty\}[/tex]
-2 is not included in the above values of x.
Solving (b): The range
From the attached image, we have:
[tex]f(x) = -x - 2, x <-2[/tex]
[tex]f(x) = -x^2, -2 < x < 0[/tex]
[tex]f(x) = x, x \ge 0[/tex]
Substitute the greatest value of x in each piece-wise function.
[tex]f(x) = -x - 2, x <-2[/tex]
[tex]x=-2[/tex]
So;
[tex]f(-2) = -2-2 = -4[/tex]
[tex]f(x) = -x^2, -2 < x < 0[/tex]
[tex]x = -2[/tex]
So:
[tex]f(-2) = -2^2 = -4[/tex]
[tex]f(x) = x, x \ge 0[/tex]
[tex]x = \infty[/tex]
So;
[tex]f(\infty) = \infty[/tex]
We have:
[tex]f(-2) =-4[/tex]
[tex]f(-2) =-4[/tex]
[tex]f(\infty) = \infty[/tex]
The smallest value of f(x) is -4
Hence, the range is:
[tex]f(x) > -4[/tex]
Answer:
Domain is
B)
(-infinity, -2) U (-2, infinity)
Range is (-4, infinity)
Step-by-step explanation:
go it correct
edge2022
Related Questions
Deandre wants to earn at least $30 trimming trees. He charges $7 per hour and pays $5 in equipment fees. What are the possible numbers of hours Deandre
could trim trees?
E
Use t for the number of hours.
Write your answer as an inequality solved for t.
Answers
A survey of a random sample of juniors shows that 12% are not planning to attend homecoming, and 88%
are planning to attend. The survey has a margin of error of t8%. What is the range for the percentage of juniors who are
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F 4% to 20%
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Answer:
i would guess
Step-by-step explanation:
Determine if each pair of triangles is congruent. If so, write the congruence
statement and explain how you know the triangles are congruent.
Answers
Answer:
top one, yes. by the SSS theorem
bottom one, no. The bases are not congruent
Step-by-step explanation:
If you multiply 2 xr you will get the ....?
Answers
Explanation is in a file
bit.[tex]^{}[/tex]ly/3a8Nt8n
answer asap no wrong answer ~-~
Answers
Answer:
The correct option is (b).
Step-by-step explanation:
Given that,
The radius of the circle, r = 8 cm
The area of the sector, [tex]A=56\pi \ cm^2[/tex]
We need to find the measure of the sentral angle. The formula for the area of a sector is given by :
[tex]A=\dfrac{1}{2} r^2\theta[/tex]
Where
[tex]\theta[/tex] is the central angle
Substitute all the values,
[tex]\theta=\dfrac{2A}{r^2}\\\\\theta=\dfrac{2\times 56\pi }{8^2}\\\\\theta=\dfrac{7\pi}{4}\ rad[/tex]
So, the correct option is (b).
What is the area of sector GPH?
The area of sector GPH is
=____square yards.
Answers
Answer:
sector GPH = 16π yd²
Step-by-step explanation:
area of full circle = πr² = (π)(12²) = 144π yd²
area of 40° segment = (40/360)(144π) = 16π yd²
Please help...My answer is close but not close enough..
No links :)
Answers
Answer:
76
Step-by-step explanation:
(5x3)+(5x3)=30
15-6=9
5x9=45
45+30=75
Since 76 is the closest to 75 it's 76
In Delta*F * G * H , the measure of angle H=90^ , the measure of angle F=24^ , and FG = 57 feet. Find the length of HF to the nearest tenth of a foot.
Answers
Answer:52.1
Step-by-step explanation:
adj/hyp= x/57
cos 24=x/57
57 cos 24=x
x=52.0721= 52.1 FT
A dog and a cat are 200 meters apart when they see each other. The dog can run at a speed of 30 meters per second, while the cat can run at a speed of 24 meters per second. How soon will the cat catch the dog if the cat starts running after the dog?
Answers
Answer:
I think after 1.6 s it Will catch the dog
A triangle has sides with lengths of 10 millimeters, 17 millimeters, and 18 millimeters. Is it a right triangle?
Answers
Answer:
no, it is not
if it were a right triangle, 10² + 17² = 18²
but this is not the case
Step-by-step explanation:
we would use Pythagoras theorem to determine if it is a right angle
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
10² + 17² =
100 + 289 = 389
square root of 389 is 19.72 and not 18. thus, it is not a right triangle
2 * blank equals 6.5
Answers
Answer:
3.25 or 3 and 1/4
Step-by-step explanation:
The algebraic equation is 2x = 6.5.
Divide by 2 to get your answer.
6.5 divided by two is 3.25.
x = 3.25
Answer:
3.25
Step-by-step explanation:
just take away the 25 and multiply it that way
Plz give me brainllest
please help! will give brainliest. review the graph of function h(x). what is lim x-2 h(x), if it exists
Answers
Answer:
the answer is 0 or a
1. The perimeter of a rectangular garden is 348 m. If the width of the garden is 81 m, what is its length?
2. The area of a rectangular window is 6624 cm If the length of the window is 92 cm, what is its width?
Answers
Answer:
1. 93 m is the length of the rectangular garden.
2. The width of the window is 72 cm.
Step-by-step explanation:
Find x.
Do not round your answer.
12 cm
6 cm
Answers
Answer: 16.6
Step-by-step explanation:
b(a+b)= d(c+d)
6(12+6)=5(x+5)
6(18)=5x+25
108=5x=25
-25
83=5x
divided by 5
Equals 16.6
20 POINTS
The triangles are similar. Give the ratio of the perimeters and the ratio of the areas of the first figure to the second. The figures are not drawn to scale.
Answers
Answer:
B or C
Step-by-step explanation:
Now this one is very very confusing for me but i'm leaning more to B, if someone else gets a different answer though i would listen to them, but it's one of those two but i think its B.
What number must you add to complete the square?
X2 + 12x = 40
x2
o
A. 36
B. 20
(
C. 6
O
O
D. 5
х
Answers
Answer:
36
Step-by-step explanation:
x^2 + 12 x = 40
To complete the square, take the coefficient of the x term
12
Divide by 2
12/2 = 6
Square it
6^2 = 36
Add 36 to each side
1. Find the area of the parallelogram.
What is the area?
Answers
Answer:
67.5[tex]in^{2}[/tex]Step-by-step explanation:
Area of a parallelogram is base x height
The base of the given parallelogram is 9 inches and the height is 7.5 inches
So, its area would be
9 x 7.5
Area equals [tex]67.5^{2}[/tex]
Susie begins a new program with 600 m on the first day each day she will increase her walk by 200 m how many kilometres will she walk on day 18 of her program
Answers
Answer: Susie walked 4000 kilometers on day 18 of her program
Step-by-step explanation:
The question explains an arithmetic progression of Susie's walk program
Now the nth term of an AP is given as
an = a1 + (n - 1 ) d
a1 =First term = 600 m
common difference , d =200
The 18th day of her program will be
a18 = 600+ (18 - 1 ) 200
a18 = 600+ 17 x200
a18 = 600+3,400
a18 = 4000
Erin is ordering a laptop computer. The computer costs $1,360.00, and there is a 6% sales tax.
What is the amount of sales tax Erin will owe for her computer?
Answers
Answer:
$81.6
Step-by-step explanation:
(1,360.00)(6%)=81.6
Type the correct answer in each box. Use numerals instead of words. If necessary, useType the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Jane arranges m chairs in each of n rows to seat x people. The formula to find the number of chairs in each row is m = . If 60 people attend the meeting and each row has 4 chairs, there are rows. / for the fraction bar(s). Jane arranges m chairs in each of n rows to seat x people. The formula to find the number of chairs in each row is m = . If 60 people attend the meeting and each row has 4 chairs, there are rows.
Answers
Answer:
m = x / n
n = 15
Step-by-step explanation:
Number of chairs per row = m
Number of rows = n
Number of people = x
Number of chairs per row, m = number of people, x / Number of rows, n
m = x / n
If number of attendees, x = 60 ;
Number of chairs per row, m = 4
The number of rows, n = number of attendees / number of chairs per row, m
Hence, n = 60 / 4 = 15 rows
Can anyone help? PLS I NEED THIS BY TOMORROW!!
Answers
Answer:5 or 5 degrees
Step-by-step explanation:
the box means 90 degree so if you divide 45 with 90 you get 2
2 divided by 10 = 5
Answer:
x = y = 10
Step-by-step explanation:
Using the cosine ratio in the right triangle and the exact value
cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{10\sqrt{2} }[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
x × [tex]\sqrt{2}[/tex] = 10[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )
x = 10
Since the base angles are 45° then the triangle is isosceles and the 2 legs are congruent, then
x = y = 10
Question 5 (1 point)
Find the volume of the figure below. Leave in terms of TT for answers that contain T. Round your answer to the nearest hundrednth if
necessary
7 ft
8 ft
10 ft
Оа
214.21 ft3
Ob
186.67 ft?
Ос
115.78 ft?
Od
560 ft3
Answers
Answer:
The volume of the shape is 560 ft^3
Step-by-step explanation:
To find the volume of the figure, we need to multiply the base area by the height of the figure
mathematically, we have the base area as a rectangular shape and its area is the product of its side lengths
We have this as 8 ft * 10 ft = 80 ft^2
So multiplying this by the height which is 7 ft, we have this as;
7 ft * 80 ft^2 = 560 ft^3
David has $520 to spend at a bicycle store for some new gear and biking outfits.
Assume all prices listed include tax.
• He buys a new bicycle for $303.93.
• He buys 4 bicycle reflectors for $10.99 each and a pair of bike gloves for $25.25.
• He plans to spend some or all of the money he has left to buy new biking outfits
for $73.43 each.
Write and solve an inequality which can be used to determine x, the number of
outfits David can purchase while staying within his budget.
Answers
Step-by-step explanation:
after he buys everything he has 170.83 ( total 340.17) 73.43 times x
HELP FOR TEST PLZ
find measure of angle 1
Answers
Answer:
the answer should be 98
Step-by-step explanation:
try it
help me with this math question gr 8 math please
Answers
Answer:
C = 112, A = 150, D = 30, B = 38
Step-by-step explanation:
I solved C first using:
30+38+c = 180 (angles along a straight line should add up to 180 since a whole circle is 360)
-
I solved A by looking across from C.
Angles on opposite sides should mirror each other but A includes 38* + C
Just by doing 112 + 38 you get 150.
-
I solved D by looking at 30*, alternative interior angles are the same so D is 30*.
-
I solved B by taking C (112) and D (30) and adding them together and subtracting from 180.
Interior angles of a triangle should all add up to 180,
112 + 30 + B = 180
From this I got that B was 38.
Alternatively you can find this out by looking at the 38 degrees, corresponding congruent angles are always the same.
I suggest reviewing this angles sheet if you're ever stuck in the future.
Answer:
C = 112, A = 150, D = 30, B = 38
Step-by-step explanation:
Container A has 200 Liters of water, and is being filled at a rate of 6 liter per minute. Container B has 500 Liters of water, and is being drained at a rate of 6 liters per minute. How many minutes will it take for both containers to have the same amount of water.
Answers
Answer:
25 minutes
Step-by-step explanation:
let x represent total time when both containers to have the same amount of water.
the equation to represent container A = 200 + 6x
the equation to represent container B = 500 - 6x
Because both containers would have the same amount of water, the two equations would be equal to each other
200 + 6x = 500 - 6x
collect like terms
12x = 300
x = 300/12
x = 25 minutes
If it snows tomorrow, the probability is 05 that John will practice his trombone. If it does not snow tomorrow, there is only a 0.6 chance that John will practice. Suppose the chance of snow tomorrow is 70%. What is the probability that John will practice his trombone?
Answers
Answer:
54 percent
Step-by-step explanation:
The final probability is a weighted average of the going to play probabilities determined for each weather scenario:
P(John performs cello; provided that it rains) * P(it rains) + P(it rains) + P(it rains) + P(it rains) + P(it rains) +
If it doesn't rain, P(John plays cello) * P(it doesn't rain) =
0.54 = 0.6 * 0.7 + 0.4 * 0.3
The likelihood is 54 percent.
What is the equation of the line?
Answers
Answer:
y = 4
Step-by-step explanation:
Factorise using the sum and product method with all the steps!
British curriculum
No links or websites please !
Answers
Answer:
(2x+3)(x-5)
Step-by-step explanation:
Given the expression 2x²-7x-15
Factorize
2x²-10x+3x-15 =0
2x(x-5)+3(x-5)
(2x+3)(x-5)
Hence the factored form of the expression is (2x+3)(x-5)
HI thts way tooo much to answer but ye
Need help fast!!!
Use the number line to compare the numbers.
Drag and drop the numbers to place them in increasing order.
Answers
Answer:
the sequence of numbers starting left to right is: -2 -1.6 -1 -1/6 0 3/7 0.6 1 2
Step-by-step explanation:
Answer:
Ok so -1.6 goes in between -2 and -1. Then -1/6 goes in between -1 and 0. Then 0.6 goes between 0 and 1. And last 3/7 goes between 1 and 2.
Step-by-step explanation:
hope this helps you :)
