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 1

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]

Study The Function Below And Then Answer The Questions That Follow. Equation What Is The Domain Of F(x)?
Answer 2

Answer:

Domain is

B)

(-infinity, -2) U (-2, infinity)

Range is (-4, infinity)

Step-by-step explanation:

go it correct

edge2022


Related Questions

Ginny has a cell phone plan that charges a flat fee of $20 per month plus $.10 per minute used talking on the phone. Which expression will calculate Ginny’s bill if she spends (t) minutes on the phone each month?

Answers

Answer:

20 + 0.10t

Step-by-step explanation:

The 20 is the flat rate, the .10 is the per minuet rate meaning the answer is 20 + 0.10t. plz 5 str and thx, and brailiest.

Find the missing length indicated in the figure.

Answers

Answer:

45

Step-by-step explanation:

Since the lines of hypotenuse are parallel,the triangles are similar

20/8 = x/18

cross multiplication

8x = 20x18

8x=360

x=45      

A dozen cookies is on sale for $1.92. How much is one cookie?
Select the answer that shows what you need to do mathematically to answer this question.
Reminder: There are 12 cookies in a dozen.

Answers

Divide total price by number of cookies:

1.92/12 = 0.16

Each cookie cost $0.16

Answer:

Step-by-step explanation:

16 cents each cookie :3

plz answer this ill give 10pts

Answers

whats the question....?

PLEASEE HELPPP ME I needdd helppp

Answers

Answer:

5

Step-by-step explanation:

divide the figure as a triangle and a rectangle first.

take away the rectangle part and if you just look at the triangle part,

you can get x using Pythagorean theorem.

Pythagorean theorem is a^2 + b^2 = c^2,

so 3^2 + 4^2 = x^2.

If you calculate it, x should be root 25, which equals 5.

So, the answer is 5.

You submitted the first number take always all of theme add 30 and your Answer will be 132

What is the area of this triangle?

Answers

Answer:

The answer would be 14 units.  

Step-by-step explanation:

Count each of the units to find the height and base.

Height - 4 units

Base - 7 units.

Then use the formula A = 1/2*h*b

A = 1/2*7*4

A = 1/2*28

A = 14 units.

The area of the given triangle is 14 units².

Use the concept of the triangle defined as:

A triangle is a three-sided polygon, which has three vertices and three angles which has a sum of 180 degrees.

And area of triangle = (1/2)x base x height

In the given triangle:

Width  = 5 units + 2 units

Width  = 7 units

Height = 2 units + 2 units

Height = 4 units

Put the values into the above formula of area,

Area of triangle = (1/2)x 7 x 4

Area of triangle = 14 unit²

Hence,

The area of the given triangle is 14 units².

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ6

True or false

A chance event with probability 1 is certain to happen

Answers

Answer:

True, since 1 is 1/1, which is 100%

Hope that helps! :)

Step-by-step explanation:

Write parametric equations of the line a. Please select the best answer from the choices provided A

Answers

Answer:

Parametric Equation of a Line

Step-by-step explanation:

A line, parallel to vector (a,b,c) passing through point P (x1,y1,z1) is represented by parametric equations

x = x1+ at

y = y1 + bt

z = z1 + ct

someone please please help me with this ! I would really appreciate it

Answers

Answer:

Both volumes are the same

Step-by-step explanation:

Volume of cylinder = [tex]\pi[/tex][tex]r^{2} h[/tex]

r = radius

h = height

Since area of the circle is given on top,

Area of a circle = [tex]\pi[/tex][tex]r^{2}[/tex]

We know the area is 12

12 = [tex]\pi[/tex][tex]r^{2}[/tex] (we need to find r)

r = [tex]\sqrt{\frac{12}{\pi} }[/tex]

r = 1.954

Now we can find the cylinder's volume:

Volume of cylinder = [tex]\pi[/tex][tex](1.954)^{2}[/tex] (6)

Volume of cylinder = 72

To find the volume of the cuboid, we use

Volume of cuboid = lwh

l = length

w = width

h = height

Volume of cuboid = 6 x 4 x 3

Volume of cuboid =  72

This proves that both the volumes are the same.

Help me plz I don’t get it

Answers

Answer:

3.33

Step-by-step explanation:

each cube represents 1, so each flat represents 0.1 and each unit represents 0.01. so if there are 3 of each, it would be 3+0.3+0.03 which equals 3.33

Answer:

3.33

Step-by-step explanation:

Each cube in this picture is equal to 1 unit as the diagram in the upper right corner shows.

We have 3 cubes so -> 1 + 1 + 1 = 3

We also have 3 squares that are 1/10th of a cube.

1/10 * 1 = 0.1  so each square is equal to 0.1 unit.

We have 3 squares so it would be 0.1 + 0.1 + 0.1 = 0.3

We have 3 tiny squares that are 1/100th of a cube.

1/100 * 1 = 0.01 so each tiny square is equal to 0.01 unit.

We have 3 tiny squares so it would be 0.01 + 0.01 + 0.01 = 0.03

Add everything up: 3 + 0.3 + 0.03 = 3.33

Simplify:............​

Answers

[tex] - \frac{4 {m}^{2} }{1 + {m}^{4} + {m}^{8} } [/tex]

is your answer

Answer:

jshdgdhdhdhdhdhdhd English project work

I need help ppl this is due tomorrow thank yooou

Answers

Answer:

8.62

Step-by-step explanation:

Use the Pythagorean theorem.

b= [tex]\sqrt{c^{2}-a^{2} }[/tex]

b=[tex]\sqrt{10.5^{2}-6^{2} }[/tex]

b= [tex]\sqrt{110.25-36[/tex]

b=[tex]\sqrt{74.25}[/tex]

b= 8.62

To solve you have to use Pythagorean Theorem:
a^2+b^2 = c^2
You’re looking for b so the formula would be:
b^2 = c^2-a^2
10.5^2-6^2
110.25-36
74.25
The square root for 74.25 is 8.61684396...
But it tells you to the nearest tenth so the answer would be 8.6

1. What shapes are formed?
2. How many triangles are formed?
3. Can two triangles fit in one cartolina which shape is a rectangle?

Answers

Answer:

1.) rectangle and triangle

2.)4 because 2 for each rectangle

3.)yes and a rectangle has 4 vertics and 4 sides and 2 equal lengths

the volume of the square pyramid is ___ cubic feet.

Answers

28ft

dkdkdk

dkdkdkdkdkdkd

ddjdjddddddddddddddddddddddddddddddddddddddddd

4 divided by 1/6 with explanation !

Answers

Multiply 4x6 all u do

54 can be divided with no remainder by which of the following numbers 2 3 4 5 6 9 10​
LINKS WILL BE REPORTED NOT HAVING IT

Answers

Answer:

6 and 9

Step-by-step explanation:

6 x 9 = 54

A number multiplied by 7 is less than 21. Which of the following expressions correctly identifies this sentence?

Answers

Answer:

Step-by-step explanation:

answer question for 10 points and brainilest

Answers

Answer:

343

Step-by-step explanation:

[tex]\frac{(7^4)^2}{7^5}[/tex]

[tex]=\frac{7^4^*^2}{7^5}[/tex]

[tex]=\frac{7^8}{7^5}[/tex]

[tex]=7^8^-^5[/tex]

[tex]=7^3[/tex]

[tex]=7*7*7[/tex]

[tex]=343[/tex]

*PLEASE HELP ASAP ITS A TEST* How many solutions does the system of linear equations represented in the graph below have?

Answers

Answer:

0

Step-by-step explanation:

The 2 lines never intersect so there are 0 solutions

find the measure of each angle

Answers

Answer:

Step-by-step explanation:

m∠ 1  =  180 - 117

m∠ 1  = 63

m∠2 = the same as m∠ 1

m∠2 = 63

m∠3 is also the same b/c of the same length of the "legs" of the triangle

m∠3 = 63

Which other expression has the same value as (-4) - (-8) ?

A. (-4) + 8
B. -4 - (-8)
C. 4 + (-8)
D. (-4 ) + (-8)

Answers

the answer is: A (-4)+8

Answer:

the answer is option (A) . (-4) + 8

Please help me check if it's right! Please give the right answers!

Answers

Answer

15

Step-by-step explanation:

12-3²+6÷(10÷5)x2²

12-9+6÷2x4

12-9+3x4

12-9+12

3+12

15

This is the only one I saw wrong. you added wrong

The parent function y = -2x^2+5 is translated down 12 units and left 8 units. What is the new equation in vertex form?

Answers

Answer:

y=-2(x+8)²-7

Step-by-step explanation:

Given: y=-2x²+5

After transformations: y=-2(x+8)²-7

Vertex would be (h,k) -> (-8,-7) instead of (0,5)

A space probe flies by a planet in an hyperbolic orbit. It reaches the vertex of its orbit at (5,0) and then travels along a 2 path that gets closer and closer to the line y=-x. Write an equation that describes the path of the space probe if the 5 center of its hyperbolic orbit is at (0,0).​

Answers

Answer:

[tex]\frac{2x^{2} }{{25} } + \frac{2y^{2}}{{25} } = 1[/tex]

Step-by-step explanation:

Since the required hyperbola has its vertex at (5,0), its transverse axis is on the x-axis and center at (0,0).

So, we use the equation in standard form

[tex]\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } = 1[/tex]

Also, since the path of the space probe gets closer to y = -x, this is the asymptote to the hyperbola.

Our standard asymptote equation is y = ±bx/a taking the negative sign and comparing with y = -x,

-bx/a = -x ⇒ b/a = 1 ⇒ a = b

Also, the coordinate of the vertex (c, 0) = (5, 0) and c² = a² + b²

substituting c = 5 and a = b into the equation, we have

c² = a² + b²

5² = a² + a²

25 = 2a²

a² = 25/2

a = √(25/2)

a = ±5/√2

rationalizing, we have

a = ±5/√2 × √2/√2

a = ±5√2/2

Since a = b, b = ±5√2/2

Inserting a and b into the equation for the hyperbola, we have

[tex]\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } = 1\\\frac{x^{2} }{(\frac{5\sqrt{2} }{2} )^{2} } + \frac{y^{2} }{\frac{5\sqrt{2} }{2} ^{2} } = 1\\\frac{x^{2} }{\frac{25 X 2 }{4} } + \frac{y^{2} }{\frac{25X2 }{4} } = 1\\\frac{x^{2} }{\frac{25}{2} } + \frac{y^{2} }{\frac{25}{2} } = 1\\\frac{2x^{2} }{{25} } + \frac{2y^{2}}{{25} } = 1[/tex]

So, the required equation is

[tex]\frac{2x^{2} }{{25} } + \frac{2y^{2}}{{25} } = 1[/tex]

I don't know this questions so pls help

Answers

Answer:

The distance between the two points is 6.3 units

Step-by-step explanation:

Here, we want to find the distance between the two points

We have the equation to find this as follows;

D = √((x2-x1)^2 + (y2-y1)^2

where (x1,y1) = (-4,2) and (x2,y2) = ((2,4)

so we have the length calculated as follows;

D = √(2-(-4))^2 + (4-2)^2

D = √6^2 + 2^2

D = √36 + 4

D = √40

D = 6.3 units

A circle has a circumference of 2 x cm. Which statement about the circumference and area is true?
O A comparison of the area and circumference is not possible since the area cannot be determined.
The numerical values of the circumference and area of the circle are equal.
O The numerical value of the circumference is greater than the numerical value of the area.
O The numerical value of the circumference is less than the numerical value of the area.
Vx
Mark this and retum
Save and Exit
Next
Submit

Answers

Answer:

O The numerical value of the circumference is less than the numerical value of the area.

Step-by-step explanation:

as pi>2, therefore, only 'the numerical value of the circumference is greater than the numerical value of the area. The numerical value of the circumference is less than the numerical value of the area' is correct.

Can someone fill this out? I am very busy today and I need someone to fill this out.

Answers

Answer:

Uh i think its a uhhh carrot

Step-by-step explanation:

A rectangle has a height of 5 inches and a area of 35 squared inches what is the length of the base of the rectangle? Please help I dont get it.

Answers

Answer:

The length of the base of the rectangle is 7 inches

Step-by-step explanation:

The Area of the rectangle can be found out by multiplying length with the breadth

Area= length *  breadth

35 squared inches= x *5

5x= 35

x= 35/5

x= 7inches

Hence the length of the base of the rectangle is 7 inches.

If the area and one side are known then we can simply find the 2nd side by simply substituting x in its place and solving the equation.

The ratio of dogs is 5:3. If there are 12 cats, how many dogs are there? PLS HELP

Answers

Answer:

First of all, is it the ratio cats to dogs or dogs to cats?

Step-by-step explanation:

?????

There are 20 dogs. To find this, do 5/3=x/12. Then solve the equation.
60 = 3x
Divide by 3
x = 20

Achilles ordered a pizza with 16 slices. Every hour, he ate half of the remaining slices. Let f(n) be the number of slices Achilles ate in the hour since he got home.

Answers

Consider we need to find f(n).

Given:

Achilles ordered a pizza with 16 slices.

Every hour, he ate half of the remaining slices.

To find:

The function f(n) that is the number of slices Achilles ate in the hour since he got home.

Solution:

Initial number of slices = 16

Every hour, he ate half of the remaining slices. So, the number slices Achilles ate in the hour since he got home are:

8, 4, 2, 1, ...

It is a geometric sequence with first term 8 and common ratio [tex]\dfrac{1}{2}[/tex].

The explicit formula for a geometric sequence is:

[tex]f(n)=ar^{n-1}[/tex]

Where, a is the first term and r is the common ratio.

Substituting [tex]a=8,r=\dfrac{1}{2}[/tex], we get

[tex]f(n)=8\left(\dfrac{1}{2}\right)^{n-1}[/tex]

Therefore, the  function f(n) that is the number of slices Achilles ate in the hour since he got home is [tex]f(n)=8\left(\dfrac{1}{2}\right)^{n-1}[/tex].

Other Questions
Please help with these questions! Who were the Allies and Axis in ww2? Find the perimeter of the figure. Round all figures to the nearest hundredths place.Isosceles trapezoidA 70.24 ftB 74.48 ftC 79.42 ftD 92.84 ft The problem with plastic bags isn't just where they end up, it's that they never seem to end. Which words should be emphasized in the sentence above?a.with, theyc.problem, never, endb.problem, endd.with, just, seem Excerpt from Miss Peregrines Home for Peculiar Children By Ransom Riggs I picked up the flashlight and stepped toward the trees. My grandfather was out there somewhere, I was sure of it. But where? I was no tracker, and neither was Ricky. And yet something seemed to guide me anywaya quickening in the chest; a whisper in the viscous airand suddenly I couldnt wait another second. I tromped into the underbrush like a bloodhound scenting an invisible trail. Its hard to run in Florida woods, where every square foot not occupied by trees is bristling with thigh-high palmetto spears and nets of entangling skunk vine, but I did my best, calling my grandfathers name and sweeping my flashlight everywhere. I caught a white glint out of the corner of my eye and made a beeline for it, but upon closer inspection, it turned out to be just a bleached and deflated soccer ball Id lost years before. I was about to give up and go back for Ricky when I spied a narrow corridor of freshly stomped palmettos not far away. I stepped into it and shone my light around; the leaves were splattered with something dark. My throat went dry. Steeling myself, I began to follow the trail. The farther I went, the more my stomach knotted, as though my body knew what lay ahead and was trying to warn me. And then the trail of the flattened brush widened out, and I saw him. What is the main idea? A. The narrator is searching in the woods.B. Grandpa is lost in the woods.C. The narrator is worried and searching for Grandpa.D. Something has happened to Grandpa. Unit 11: Value & Surface Area Homework 1: Area of planes FigurePls Help me with #11 A school is holding its annual book fair. The line plot below shows the amount of books students have boughtWhat is the experimental probability that a student will buy 3 books?A.4/15B.3/15C.4/3D.4/9 Give anexample of a bioindicator, and explain why they are important. Anybody know which one goes in each PLS HELP FAST!!!! Determine the new concentration if you dilute 500mL of a 1.9M solution of NaCl to 1L. Find the volume of the composite solid. Write your answer as a decimal. If the DNA code for the amino acid alanine is CGA, the tRNA anticodon for alanine is ?1.)AGC2.)CGA3.)CGT4.)GCU 10. Aqua means "water" or "a light blue color." Marine refers to the sea. Use this informationto determine what the gemstone aquamarine might look like.Determine what the gemstone aquamarine might look like? What information does not affect whether a credit card company will give you a card? O A. How many credit cards you already have O B. How much debt you have O C. Your payment history D. Which companies you have credit cards from already SUBMIT i cant figure out 8 to the power of 7 over 8 to the power of -2 solve the system using elimination y = -x10x + 2y = 40 You have a cold gas of atoms, and you observe that if you shine light consisting of photons with energy 10 eV through the gas, some free electrons are observed, implying that a photon of this energy is able to ionize an atom in the gas. (a) If you find that the emitted electrons from the gas have a kinetic energy of 1 eV, what is the ionization energy of the cold atom Cameron and some friends are going to the movies. At the theater, they sell a bag of popcorn for $5.50 and a drink for $3.75. How much would it cost if they bought 3 bags of popcorn and 6 drinks? How much would it cost if they bought pp bags of popcorn and dd drinks? When rolling a number cube, what is the probability of rolling a 2 or an even number. Express your answer as a fraction in lowest terms what are some examples of advanced cities?