1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
stiv31 [10]
3 years ago
15

Place each of the key aspects under the function it describes

Mathematics
2 answers:
melamori03 [73]3 years ago
5 0

Answer:

range: {y: y ≥ 0} ⇒ h(x)

decreasing over(-∞ , 1) ⇒ h(x)

increasing over (-∞ , 0) ⇒ g(x)

range: {y: y ≤ 1} ⇒ g(x)

increasing over (1 , ∞) ⇒ h(x)

decreasing over(0 , ∞) ⇒ g(x)

Step-by-step explanation:

∵ h(x) = (x - 1)²

∴ Its vertex is (1 , 0)

∴ The parabola is opened upward

∴ The range: {y: y ≥ 0}

∴ It's decreasing over (-∞ , 1)

∴ It's increasing over (1 , ∞)

∵ g(x) = -(x - 1)(x + 1) = -(x² - 1) = -x² + 1

∴ Its vertex is (0 , 1)

∴ The parabola is opened downward

∴ The range: {y: y ≤ 1}

∴ It's increasing over (-∞ , 0)

∴ It's decreasing over (0 , ∞)

RideAnS [48]3 years ago
5 0
<h2>Answer with explanation:</h2>

First function h(x) is given by:

h(x)=(x-1)^2

The function is a quadratic function

and also we know that:

(x-1)^2\geq 0

Hence, the range is: {y | y≥0}

Also, we know that the graph of the function decreases continuously in the interval (-∞,1) and then it increases continuously in the interval (1,∞)

and the vertex is at (1,0)

Second function is:

       g(x)=-(x+1)(x-1)

which could also be written by:

g(x)=-(x^2-1)

since we know that:

(a+b)(a-b)=a^2-b^2

Also,we know that:

x^2\geq 0\\\\x^2-1\geq -1\\\\-(x^2-1)\leq 1

i.e.

g(x)\leq 1

Hence, we get the range of this function is:  {y | y≤1}

The graph of this function is a downward open parabola with vertex at (0,1) and hence, the graph is increasing in the interval (-∞,0) and decreasing over the interval (0,∞).

You might be interested in
How many ounces are in a pound?
Naddika [18.5K]
16 ounces is the correct [email protected]
4 0
3 years ago
I need help with all the ones that don't have answers.
zlopas [31]
<em>- What two consecutive odd integers have a sum of 48</em>?

23 + 25 = 48

- <em>Two negative consecutive integers have a sum of -45. What are the integers?
</em>
<em />-22 + -23

- <em>The sum of two consecutive integers 75. What are the two integers?</em>

37 + 38 = 75

- <em>What <u>three</u> consecutive odd  integers have a sum of 81?
</em>
<em />25 + 27 + 29 = 81

Hope I could help! Have a good one. I believe that is all of the unanswered questions. If I missed one, let me know!<em />
7 0
3 years ago
A manufacturer has 5,634 pens to divide into packs of 4 pens. The manufacturer makes as many packs as possible.
Pachacha [2.7K]

Answer:

1,408 packs can be made, and 2 pens will be left out.

Step-by-step explanation:

Given that a manufacturer has 5,634 pens to divide into packs of 4 pens, and the manufacturer makes as many packs as possible, to determine how many packs of pens does the manufacturer make, and how many pens are left over, the following must be done calculation:

5.634 / 4 = X

1,408.5 = X

5,634 - (1,408 x 4) = X

5.634 - 5.632 = X

2 = X

Therefore, 1,408 packs can be made, and 2 pens will be left out.

4 0
3 years ago
The area of a rectangular flower bed is 24 square feet. The perimeter of the same flower bed is 22 feet. What are the dimensions
Gennadij [26K]
The dimensions of the flower bed are 8 and 3

The area is 8•3= 24

And 8+8+3+3= 22

5 0
3 years ago
Can someone please help me.. answer choices below<br> A.46<br> B.134<br> C.136<br> D.146
Vesnalui [34]
C b/c 180° - 44° = 136°. Angles DEB & AED add up to 180° b/c they are supplementary angles.
3 0
3 years ago
Read 2 more answers
Other questions:
  • a container is filled with 100 grams of bird feed that is 80% seed. How many grams of bird feed containing 5% seed must be added
    15·1 answer
  • Penelope is making cards for her family members. she completed 9/16 of the cards on Monday and 2/16 of the cards on Tuesday what
    11·1 answer
  • Y equals 7.75x fourmovie tickets cost how many dollars remember X represents the number of movie tickets
    10·1 answer
  • Round each number to the nearest whole number.  What is the best estimate for the answer to 276.37 – 67.81?   A. 209   B. 208.6
    13·2 answers
  • A rectangular cardboard has dimensions as shown. The length of the cardboard can be found by dividing its area by its width. Wha
    12·2 answers
  • After 1 year, the value of a car decreases by 19%. The car is now worth £3078. What was the value of the car originally?​
    14·1 answer
  • Waiting times to receive food after placing an order at the local Subway sandwich shop follow an exponential distribution with a
    14·1 answer
  • Find the value of a and b
    7·1 answer
  • Please help me with this question
    12·1 answer
  • A function has factors of (x-2) and (x + 3) which graph could represent the function
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!