Which transformations would affect the starting point of a square root
function?

Answers

Answer 1

Answer:

There are at least two transformations that would affect the starting point of a square root: (i) Horizontal translation, (ii) Vertical translation.

Step-by-step explanation:

Let the square be represented by the following function:

[tex]f(x) = \sqrt{x},\,\forall \,x \ge 0[/tex] (1)

Which means that function has only valid solutions for every element of [tex]x[/tex] greater or equal to 0. In particular, the starting point is [tex]x = 0[/tex].

We can change the starting point of this function by horizontal translation, which is defined below:

[tex]g(x) = f(x - a), \,\forall \,x \ge a[/tex] (2)

In other words, we create the resulting function:

[tex]g(x) = \sqrt{x-a}, \,\forall\,x \ge a[/tex] (3)

Another, possibility is using a vertical translation, whose definition is defined below:

[tex]h(x) = f(x)+c,\,\forall \,x \ge 0[/tex] (4)

In other words, we create the following function:

[tex]h(x) = \sqrt{x} +c[/tex] (5)

Hence, there are at least two transformations that would affect the starting point of a square root: (i) Horizontal translation, (ii) Vertical translation.


Related Questions

In ALMN, n = 910 inches, ZL=64º and ZM=31°. Find the length of 1, to the nearest
10th of an inch.

Answers

Answer:

Step-by-step explanation:

What is the area? Please hurry.

Answers

Answer:

85 cm squared

Four times the quotient of 3 and 4

Answers

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

The quotient of 3 and 4 is 0.75.

3/4 = 0.75

--

0.75 x 4 = 3...

So the answer is 3.

Nurses at a hospital weigh five newborn babies and round the weights to the nearest whole number. Which of the weights round to 8 pounds?

Answers

The first one third one and last one

The equation y=9x represents the total cost y for x movie tickets.
A.In this situation,which quantity is dependent and which is
independent? Justify your answer.

B.Eight friends want to go see a movie.what would the total cost be,explain how u found the answer.

Answers

Answer:

A) y or total cost is the dependent variable and x which is the number of movie tickets is the independent variable. Y is called dependent because its value depends on the value of x.

B) So 8 is the number of tickets which is X. So x=8. The total cost y will be: 8x9= 72

Toronto FC have won half of their
games and lost 42% of their games.
What percentage have they tied?

Answers

I think it’s 58% could be wrong tho I’m not good at math

x/3−20=−15
what is the anwser

Answers

Answer:

x=15

Step-by-step explanation:

Describe the quadratic function:
f (x) = (x - 7)^2

Answers

Answer:

Step-by-step explanation:

(x-7)^2

(x-7) ( x-7)

[tex]x^{2}[/tex] -14x + 49

it's a perfect square function

Solve.

A standard coffee mug has a capacity of 16 fluid ounces.

If Annie needs to fill two mugs with coffee how many total quarts of coffee does she need?

Annie needs ____ quarts of coffee

Answers

Annie needs 3  quarts of coffee

(Please mark me brainliest! Thank you in advance!)

14. Stewart, Angela, and Thomas each prefer a different type of
book. They read history, poetry, and science fiction. Angela
does not like poetry. Thomas does not like poetry or science
fiction. Which type of book does each person like best?

Answers

Answer:

go ask your teacher

Step-by-step explanation:

solve the expression 2xdivided by 6 (x=12)

Answers

Answer:

4

Step-by-step explanation:

first you plug in 12 for x so it would then be 2(12) divided by 6 and then follow the rules of math so you would multiply 12 and 2 which is 24 then 24 divided by 6 is 4

The answer is 4. Hope this helps

A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is 25 feet more than the length of the shortest side. Find the dimensions if the perimeter is 157 feet
What is the length of the shortest side?
What is the length of the second side?
What is the length of the third side?

Answers

Answer:

shortest:  33 feet  

second:  66 feet

third:  58 feet

Step-by-step explanation:

s = shortest side  (33)

2s = second side   (66)

25 + s = third side   (58)

157 = s + 2s + 25 + s

157 = 4s + 25

4s = 132

s = 33

Danica is making a rectangular isle runner which has a length that is 8 inches more than four times the width. Create a function, A(w), for the area of the isle runner, where w represents the width in inches.

Answers

Answer:

Step-by-step explanation:

L=4W+8

A=LW, using L from above makes this

A(W)=(4W+8)W

A(W)=4W^2+8W

Help me plis

Answer
A) 30 degrees
B) 60 degrees
C)120 degrees
D) 150 degrees

Answers

This would also be 30 degrees because all angles of parallelogram are same.

Hopefully you get This right

Answer: D) 150 degrees

Step-by-step explanation:

Opposite angles in a parallelogram are equal so, if angle D is 30 degrees, angle F is also 30 degrees. This adds up to 60 degrees.

A parallelogram is a quadrilateral so the total of its angles is 360 degrees.

Subtract 60 degrees from 360 = 300

Angles E and G will be 300 divided by 2 so E is 150 degrees.

find the interest earned for $650 at 2% for 6 years

Answers

Answer:

I = $ 78.00

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 2%/100 = 0.02 per year,

then, solving our equation

I = 650 × 0.02 × 6 = 78

I = $ 78.00

The simple interest accumulated

on a principal of $ 650.00

at a rate of 2% per year

for 6 years is $ 78.00.

Answer: $78.00

the answer is 78.00

plsssssssssssssssssssss help me i need to get these right so i can play roblo.x pls tell me how you got the answer

Answers

Answer:

675 mm²

Step-by-step explanation:

base = 15 x 15  = 225 mm²

4 sides = 4(15)(15)(0.5) = 450 mm²

450 + 225 = 675 mm²

5x-8(3y+13)-1 what's the expression

Answers

Did u try looking it up?

PLEASE ANSWER WITH SUBSTITUTION
9=3x-y
6x=3y+3

Answers

Answer:

x = 8; y = 15

Step-by-step explanation:

First choose any one equation and isolate a variable of your choice

I will use the first equation and isolate variable y

9 = 3x - y

Add y to both sides to make it positive

y + 9 = 3x - y + y

Subtract both sides by 9 to isolate the variable y

y + 9 - 9 = 3y - 9

y = 3x - 9

Now that we know what expression is equal to y, we can substitute this value of y into the second equation

6x = 3(3x - 9) + 3

Use distributive property

6x = 9x - 27 + 3

Combine like terms

6x = 9x - 24

Subtract both sides by 9x

6x - 9x = 9x - 9x - 24

-3x = -24

Divide both sides by -3 to isolate the variable x

-3x ÷ -3 = -24 ÷ -3

x = 8

Plug this value of x into either equation

I will use the first equation because it is shorter

9 = 3(8) - y

9 = 24 - y

Add y to both sides to make y positive

y + 9 = 24 - y + y

y + 9 = 24

Subtract 9 from both sides to isolate the variable y

y + 9 - 9 = 24 - 9

y = 15

Which of the following expressions has a constant of 7 and a coefficient of 3?
3 + 73
7-3
7+3
31 +7

Answers

I wanna say it’s 3+73 I’m not that smart so don’t trust me

8 3/5 = -4x + 5 3/5 ??
Solution??

Answers

Answer:

x=−3/4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

435=−4x+285

Step 2: Flip the equation.

−4x+285=435

Step 3: Subtract 28/5 from both sides.

−4x+285−285=435−285

−4x=3

Step 4: Divide both sides by -4.

−4x−4=3−4

x=−34

Answer:

as a decimal: [tex]x=-0.75[/tex]

as a fraction: [tex]x=-\frac{3}{4}[/tex]

Step-by-step explanation:

note: i'm going to convert the fractions to decimals because i prefer working with decimals rather than fractions :)

[tex]8\frac{3}{5}[/tex] as a decimal is [tex]8.6[/tex][tex]5\frac{3}{5}[/tex] as a decimal is [tex]5.6[/tex]the equation is now [tex]8.6=-4x+5.6[/tex]

first, subtract 5.6 from both sides of the equation.

[tex]5.6[/tex] and [tex]-5.6[/tex] cancel each other out, leaving you with [tex]-4x+0[/tex] on the right side of the equation. it's not necessary to leave the [tex]0[/tex] in the equation, so just leave it as [tex]8.6=-4x[/tex]now subtract [tex]5.6[/tex] from the left side of the equation. [tex]8.6-5.6=3[/tex], therefore the equation is now [tex]3=-4x[/tex]

then divide both sides of the equation by -4.

you are left with [tex]x[/tex] on the right side of the equation and [tex]-\frac{3}{4}[/tex] or [tex]-0.75[/tex] on the left side of the equation, aka [tex]x=-0.75[/tex] or [tex]x=-\frac{3}{4}[/tex]

and that's it! the solution as a fraction is [tex]x=-\frac{3}{4}[/tex] and as a decimal is [tex]x=-0.75[/tex].

if you want to check the solution, just plug one of those values in for [tex]x[/tex] in the original equation. since i converted it all to decimals, i'll check my answer using [tex]-0.75[/tex] for [tex]x[/tex] in [tex]8.6=-4x+5.6[/tex].

first, plug in -0.75 for x.

[tex]8.6=-4x+5.6[/tex] ⇒ [tex]8.6=-4(-0.75)+5.6[/tex]

begin simplifying by multiplying -4 and -0.75.

[tex]-4(-0.75) = 3[/tex][tex]8.6=3+5.6[/tex]

add 3 and 5.6.

[tex]3+5.6=8.6[/tex][tex]8.6=8.6[/tex]

since both sides of the equation are equal, that means your [tex]x[/tex] value is correct and therefore a solution to the equation!! :)

i hope this helped! have a lovely rest of your day <3

contractor is building a fence around a square garden that has a side length of 3 inches in a scale drawing. The scale factor of the drawing is 1 1··2inches : 4 feet. If one link of fence measures 2 2··3feet, how many links are needed to build a fence around the entire garden?

Answers

Answer:

Step-by-step explanation:

23 beause the shade links of the garden

Answer:

Step-by-step explanation:

Each side of the square garden is 3 inches. Convert each side to sq ft. 1 1/2 x2 = 3 inches. So 4ft x 2 =8ft. 8ft. X 4 sides = 32ft perimeter that needs coverage. Each link equals 2.67 or 2 2/3. 12x2.67=32.04

12 links

twice the sum of nineteen and twenty is seventy-eight in a symbol ​

Answers

Uhm what’s your question

please help, explain if possible

Answers

Answer:

Step-by-step explanation:

133

102

136

what is 2 1/8 in simplest form​

Answers

Answer:

Check out a website called calculator soup. They've got awesome fraction calculators for all sorts of things.

Step-by-step explanation:

1 1/4 probably because I think I’ve done something like this before

Find the scale factor

Answers

Answer:

the scale factor is penguin

jkjk the scale factor is 1/2

Step-by-step explanation:

to find the scale factor you take the coordinates of the image and divide it by the coordinates of the preimage

ex. A' coordinates are (3,1)

A coordinates are (6,2)

3/6=1/2

1/2=1/2

therefore the scale factor is 1/2

hope this helps :)

Kay is interested in getting chickens so she can have fresh eggs before she buys her chickens she wants to find the mean number of eggs each one will lay she begins by
randomly selecting 40 chickens from a large poultry farm and counts how many eggs each one lays within one month she finds the mean to be 24.8 eggs with a standard deviation of 6.9 eggs the resulting interval is (22.96, 26.64) which of the following correctly interprets the 90% confidence interval for the true mean number of eggs chickens from this poultry farm may within one month?

Answers

Answer: just subtract both of the numbers and you will find it

Step-by-step explanation: hope I helped ;)

Answer:

C. (22.96, 26.64)

Step-by-step explanation:

Help me plz :)

All linear graphs have what?
1. Equal
2.Relationships
3. No Relationships
4. Negative

Answers

Answer:

2.Relationships

Step-by-step explanation:

Linear means straight and a graph is a diagram which shows a connection or relation between two or more quantity. So, the linear graph is nothing but a straight line or straight graph which is drawn on a plane connecting the points on x and y coordinates.

Suppose that $2000 is invested at a rate of 2.8%, compounded quarterly. Assuming that no withdrawals are made, find the total amount after 4 years.
Do not round any intermediate computations, and round your answer to the nearest cent. Plz answer now

Answers

Answer:

Cheese Squid

Step-by-step explanation:

according to my neurological evaluation of the current situation(s), it appears we are friends, therefore, I feel obliged to request that bring un-forth a specific set of 'roles' to my person. By which I mean, it appears having created any sort of emotional connection with you seems to reward such 'roles' as such I request that you immediately bring fourth said 'roles'Either way though there was a Neurological Enzymetive Paralastic imbalance between the code of conductional adminstrative classificationsNot funny I didn't laugh. Your joke is so bad I would have preferred the joke went over my head and you gave up re-telling me the joke. To be honest this is a horrid attempt at trying to get a laugh out of me. Not a chuckle, not a hehe, not even a subtle burst of air out of my esophagus. Science says before you laugh your brain preps your face muscles but I didn't even feel the slightest twitch. 0/10 this joke is so bad I cannot believe anyone legally allowed you to be creative at all. The amount of brain power you must have put into that joke has the potential to power every house on Earth. Get a personality and learn how to make jokes, read a book. I'm not saying this to be funny I genuinely mean it on how this is just bottom barrel embarrassment at comedy. You've single handedly killed humor and every comedic act on the planet. I'm so disappointed that society has failed as a whole in being able to teach you how to be funny. Honestly if I put in all my power and time to try and make

Answer:

Step-by-step explanation:

A = p(1+r/n)nt

A = final amount

p = principal = 2000

r = interest rate = .04

n = # times compounded pet year = 2

t = time in years = 7

A = 2000(1+.04/2)2(7)

A = 2000(1.02)14

Just plug into calculator for final amount

What is the volume of a hemisphere with a radius of 5.7 m, rounded to the nearest
tenth of a cubic meter?

Answers

Answer: 387.9 m

Step-by-step explanation:

Volume of a Sphere:

V=\frac{4}{3}\pi r^3

V=

3

4

πr

3

\text{radius} = 5.7

radius=5.7

meters

\text{Plug in:}

Plug in:

\frac{4}{3}\pi (5.7)^3

3

4

π(5.7)

3

775.734624395

775.734624395

Use calculator

\text{Volume of Hemisphere HALF of Volume of Sphere:}

Volume of Hemisphere HALF of Volume of Sphere:

\frac{775.734624395}{2}

2

775.734624395

Divide volume by 2

387.867312198

387.867312198

\approx 387.9\text{ m}^3

≈387.9 m

3

The volume of a hemisphere with a radius of 5.7 m is 193.83534 m³.

What is Volume?

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc.

Volume is sometimes referred to as capacity.

We have,

Radius = 5.7 m

So, the Volume of Hemisphere

= 2/3 πr³

= 2/3 x 3.14 x (5.7)³

= 2/3 x 3.14 x 185.193

= 193.83534 m³

Thus, the volume is 193.83534 m³.

Learn more about Volume here:

https://brainly.com/question/1578538

#SPJ2

can nyone help me with this​

Answers

Answer:

B

Step-by-step explanation:

When two triangles are congruent they will have exactly the same three sides and exactly the same three angles.

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