place each of the key aspects under the function it describes

Question

14-03-2019
Mathematics

contestada

place each of the key aspects under the function it describes

Respuesta :

Otras preguntas

What change needs to be made to sentence 11 (reproduced below) to make the sentence grammatically correct? During this voyage, Fossett also kept in touch with w

Assume the following variables have been declared: children is an int variable containing the number of children in a community families is an int variable cont

Express cos K as a fraction in simplest terms. 3 J K Answer Attempt 1 out of 2 cos K 4 5 I

Read the poem carefully. Then, in a well-written essay, analyze how Channing uses literary elements and techniques to develop a complex portrayal of the speaker

What does this mean? You are required to write a brief memorandum explaining and contrasting the roles of government, citizens, businesses, and nonprofits in t

Solve for the h in the following formula: A = 2 π r ( r h ) . Do not write h = in your answer

In a group of 20 executives 8 belong to finance department, 7 belong to operations department and the rest belong to human resources department. In another grou

1. Give the rectangular coordinates for the polar coordinates (-4, 30°). 2. Give the rectangular coordinates for the polar cordinates (3, 5π/3)

Calcule la resistencia (en Ω) de un resistor de carbón por el que circula una corriente de intensidad: 200 mAa una tensión de 220 V 3 A a una tensión de 120 mV

Which of the following is the name of the pathogen most likely causing the "same illness"? Listeria monocytogenes E. coli Norovirus Clostridium botulinum

Ashraf82 Ashraf82 · Answer 1 · 2019-03-23T23:05:47+01:00

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 , ∞)

lidaralbany lidaralbany · Answer 2 · 2019-06-26T09:40:43+02:00

Answer with explanation:

First function h(x) is given by:

[tex]h(x)=(x-1)^2[/tex]

The function is a quadratic function

and also we know that:

[tex](x-1)^2\geq 0[/tex]

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:

[tex]g(x)=-(x+1)(x-1)[/tex]

which could also be written by:

[tex]g(x)=-(x^2-1)[/tex]

since we know that:

[tex](a+b)(a-b)=a^2-b^2[/tex]

Also,we know that:

[tex]x^2\geq 0\\\\x^2-1\geq -1\\\\-(x^2-1)\leq 1[/tex]

i.e.

[tex]g(x)\leq 1[/tex]

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,∞).