Mathematics High School

State the domain, the range, and the intervals on which function is increasing, decreasing, or constant in interval notation

Answers

Answer 1

Answer:

Domain: [tex][-1,\infty)[/tex]

Range: [tex](-\infty, 3][/tex]

Decreases over: [tex](-1,-\infty)[/tex]

Step-by-step explanation:

Given

[tex]f(x) = -\sqrt{x + 1} + 3[/tex] --- Missing from the question

Solving (a): The domain

To get the domain, the expression under the square root must not be negative.

In other words:

[tex]x + 1 \ge 0[/tex]

Solve for x

[tex]x + 1 -1\ge 0-1[/tex]

[tex]x \ge -1[/tex]

Hence, the domain is:

[tex][-1,\infty)[/tex]

To get the range, we plot the values of the domain in the expression.

[tex]x = -1[/tex]

[tex]f(x) = -\sqrt{x + 1} + 3[/tex]

[tex]f(-1) = -\sqrt{-1+1} +3[/tex]

[tex]f(-1) = -\sqrt{0} +3[/tex]

[tex]f(-1) = -0 +3[/tex]

[tex]f(-1) = 3[/tex]

[tex]x = \infty[/tex]

[tex]f(\infty) = -\sqrt{\infty +1}+3[/tex]

[tex]f(\infty) = -\sqrt{\infty}+3[/tex]

[tex]f(\infty) = -\infty+3[/tex]

[tex]f(\infty) = -\infty[/tex]

So, the range is: [tex](-\infty, 3][/tex]

To get the interval where the function increases or not, we simply plot the graph of f(x).

See attachment for graph.

From the attachment, it will be observed that the graph of f(x) continuously decreases from x = -1, and it never increased.

This implies that, the graph decreases over the interval [tex](-1,-\infty)[/tex]

State The Domain, The Range, And The Intervals On Which Function Is Increasing, Decreasing, Or Constant

Related Questions

Mason recently bought seven boxes. A week later half of all his boxes were destroyed in a fire. There are now only 22 boxes left. With how many did he start with

Answers

Step-by-step explanation:

if mason had recently bought seven boxes and half of them got destroyed in a fire which is 1/2, and there are now only 22 boxes left soo im

using  based on the info it gave me sorry if its wrong

-Find the final amount of boxes left:

  -If mason had bought in seven boxes recently and after 1/2 if gone and results in 22 that should be in logic 44 since 22×2=44

  -to find the box he started with when he also  bought in 7 boxes we should be 37 and then add 7 to  get 44

The final answer is : 44

Y’all someone help pls 5x-3=21-x

Answers

5x-3=21-x
6x=24
X=4

You simply have to isolate the variable and then divide by 6 so that x is completely alone.
The answer is x=4

5x - 3 + x = 21
6x - 3 = 21
6x = 24
x = 4

what is 3/10+4/5 estimated?​

Answers

Answer:

11/10

Step-by-step explanation:

4/5 = 8/10

8/10 + 3/10 = 11/10 or 1 and 1/10

Answer:

The estimate is 1

{[(66/11) + 3 ] x2}
PLEASE HELPP

Answers

Answer:

((66/11)+)x2

(6)+3)x2

18+2

=20

Step-by-step explanation:

you can divide and copy the 2 and 3 and you times the 6x3 copy 2 then plus thats the equal of 20..

I HOPE ITS HELP THANK YOU

5x+-7(x-2) help me ty

Answers

Answer:

-2x+14

Step-by-step explanation:

simplify the equation and thats your answer


Bob, the plumber, charges the cost of materials as his labor fee. If his current job

has a material cost of $130, how much will Bob charge his client (including his labor feel?

Answers

Answer:

$162.5

Step-by-step explanation:

162.5 dollars because you divide the cost of materials by 4 and add that to 130

can someone help me please

Answers

Answer:

y= -2/5x

Step-by-step explanation:

At x=0 y is 4 and its decreasing

Use the slope equation thing

(y2-y1)/(x2-x1)

the coords for each point are (0,4) , (5,2)

Now fill it in

(2-4)/(5-0)

(-2)/(5)

-2/5x

What is the following quotient?
9+ V2
4-7

Answers

U clicked the answer already

1/5 x = 20 solve for x

Answers

Answer: x=100

Step-by-step explanation:

Let's start by multiply 1/5 on both sides to cancel it out with the x

1/5x=20

(1/5) (1/5)

x=100

1/5 MULTIPLIED BY 20 CAN ALSO BE 5 TIMES 20!

Please help urgent I’ll give Brainly if it’s right

Answers

Answer:

24

Step-by-step explanation:

4*1.5=6

6*4=24

Answer:

24

Step-by-step explanation:

4*1.5=6*4=24

Whats is the solution for the system ? Helpppp

Answers

Answer:

infinitely many solutions

Step-by-step explanation:

NO LINKS

How do I solve quadratic word problems????

Answers

You first make the quadratic equation then do the quadratic then pick the more right answer.

I will mark you brainliest for the correct answer

Please I need asap this is very important

Answers

for the first picture, the answer is the third option. for the second picture, the answer is the first option. hope this helps!

When multiplying exponent, you subtract the exponents
True or false?

Answers

Answer:When multiplying powers with the same base, you subtract the exponents. When dividing powers with the same base, you multiply the exponents

Step-by-step explanation:

Which postulate can be used to prove the two triangles are congruent?

Answers

Answer:

ASA

Step-by-step explanation:

ANGLE SIDE ANGLE IS SUITBLE

I need help finding this answer please

Answers

Answer:

aand b

Step-by-step a and b

Answer:

It is b and a you welcome

Step-by-step explanation:

Use the graph below.




Which equation represents the line that is graphed?


A

y=13x+6


B

y=13x−6


C

y=3x+6


D

y=3x−6

Answers

Answer:

Hange-san is a big fan of you :) She wants you to help her with her titan experiments! :)

Step-by-step explanation:

What is the minimum y value of the following quadratic function? f(x) = x2 - 6x + 8

Answers

Answer:

14

Step-by-step explanation:

k

=

c

−

b

2

4

a

We know that

a

=

1

,

b

=

−

8

and

c

=

2

, so let's substitute:

k

=

2

−

(

−

8

)

2

4

(

1

)

=

2

−

64

4

=

2

−

16

=

−

14

.

So, we have

min

=

−

14

. Let's check:

graph{(x^2 - 8x + 2 - y)(-14 -y)=0 [-11.82, 20.22, -15.38, 0.64]}

5m=85
I really need help!!

Answers

Answer:

5m=17

Step-by-step explanation:

You have to solve what m is.

[tex]5^{17}[/tex]

Answer:

m=17

Step-by-step explanation:

5 x 17 = 85

hope this helps!

9/12 - 1/3 ? help i will mark brainly

Answers

Answer:

decimal: 0.4166666666...

fraction: 15/36 (simplified: 5/12)

Step-by-step explanation:

Please help I’m in trouble end of the quarter is tomorrow

Answers

This is literally what I'm doing in school right now...

Answer: (A) TRUE

Mary worked from Monday to Saturday last week and bought lunch in the company’s restaurant
every day.
Her lunches cost a different amount every day.
Each lunch cost a multiple of 20¢.
The most expensive lunch of the week cost $7.60 and the cheapest one cost $4.40.
Friday’s lunch cost exactly 11⁄2 times as much as Wednesday’s lunch.
Tuesday’s lunch cost $1.20 more than Thursday’s lunch.
(a) What is the minimum total that Mary’s six lunches last week could have cost?
(b) What is the maximum total that Mary’s six lunches last week could have cost?

Answers

Answer:

25%. 4.80 divided by 1.20 = 4 x 100 = 40o%

Using logical and arithmetic principles, the minimum and maximum total Mary could spend is $31.20 and $40.40 respectively.

Cheapest lunch fee = $4.40 = 440¢Most expensive = $7.60 = 760¢

Minimum total cost of lunch :

Lunch cost will increase steadily by multiple of 20¢ from the cheapest unless given a stated constraint

Monday = $4.80

Tuesday = $4.40 + 1.20 + 0.2 = $5.80

Wednesday = $4.40

Thursday = $5.80 - $1.20 = $4.60

Friday = 3/2($4.40) = $6.60

Saturday = $5.00

Total = $(4.40 + 5.80 + 4.80 + 4.60 + 6.60 + 5.00) = $31.20

Maximum Total :

Lunch cost will decrease steadily by multiple of 20¢ from the most expensive unless given a stated constraint

Monday = $7.40

Tuesday = $7.60 + 1.20 = $6.40

Wednesday = $4.80

Thursday = $7.60

Friday = 3/2($4.80) = $7.20

Saturday = $7.00

Total = $(7.40 + 6.40 + 4.80 + 7.60 + 7.20 + 7.00) = $40.40

Therefore, the minimum and maximum total Mary could spend is $31.20 and $40.40 respectively.

Learn more : https://brainly.com/question/18963932

The slide at the playground has a height of 5 feet.
The sliding board is 13 feet long. How far away
from the ladder is the bottom of the slide?

Answers

Answer:

Assuming the slide is straight - 12 feet

Step-by-step explanation:

Assuming the slide is straight - it creates a right triangle with long side 13 feet and one of the short sides of 5 feet. We need to find the other short side.

We know that:

[tex]x^2 + 5^2 = 13^2\\x^2 + 25 = 169\\x^2 = 144\\x = 12 \vee x = -12\textrm{; but -12 doesn't make sense}[/tex]

Lamar. That is the answer. I’m playin, I suck at math

6^2 - (3 * -4) + 20
please help meeee

6^2 = six to the second power

Answers

Answer:

6^2 - (3*-4)+20

6^2 - (-12)+20

36+12+20

48+20

68

Let me know if this helps!

Answer:

68

Step-by-step explanation:

Find AC. Need help fast.

Answers

Answer:

dc

Step-by-step explanation:

i know its right

A cylindrical fish tank provides a 360° view. The height of the cylindrical fish tank is 30 inches, and the diameter of the base is 27.5 inches. If one US gallon is equal to approximately 231 cubic inches, calculate the amount of water the tank will hold.

Give you 100 more brainly points plz help

Answers

Step-by-step explanation:

I'll get the answer for you this stuff is hard

can someone tell me the graph pls i’ll give you brainlist and points plz

Answers

Answer: (0,-2)

hope that answered your question

can someone help me please

Answers

Answer:

4/3

Step-by-step explanation:

You count 4 up from (1,-1) then 3 over to (4,3).

Need help with math plz thank you

Answers

Answer:

Step-by-step explanation:

law of sines  

Sin(A) / a  = Sin(B)/b

where A = 24

a=BC

B= 59

b =AB

then

Sin(24)/a =Sin(59)/19

0.4067366 / a = 0.8571673 / 19

0.4067366 / a = 0.045114

0.4067366 / 0.045114 = a

9.015 = a

BC = 9.0 mi

What is the measurement of the angle FHG

Answers

It should be 70 lmk if it’s wrong
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