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
maxonik [38]
3 years ago
12

The function f(x) = square root of x is translated left 5 units and up 3 units to create the function g(x)

Mathematics
1 answer:
kompoz [17]3 years ago
7 0

Answer:

The domain of g(x) is {xI x > -5} ⇒ first answer

Step-by-step explanation:

* Lets talk about the transformation at first

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

* lets revise the meaning of the domain

- The domain is all values of x that make the function defined

- Find the values of x which make the function undefined

- The domain will be all the real numbers except those values

* Now we can solve the problem

∵ f(x) = √x

- f(x) translated 5 units to the left, then add x by 5

∴ f(x) ⇒ f(x + 5)

- f(x) translated 3 units up, then add f(x) by 3

∴ f(x) ⇒ f(x) + 3

- The function g(x) is created after the transformation

∴ g(x) = f(x + 5) + 3

∵ f(x) = √x

∴ g(x) = √(x + 5) + 3

- The function will be defined if the value under the square root

  is positive (means greater than 0)

∵ The expression under the square root is x + 5

∴ x + 5 > 0 ⇒ subtract 5 from both sides

∴ x > -5

- The domain will be all the real numbers greater than -5

∴ The domain of g(x) is {xI x > -5}

You might be interested in
A snowstorm began on Monday evening. It snowed steadily until 6:00 am on Tuesday morning when the snow was 12 inches deep. Kevin
poizon [28]

Answer:

what is expected at 7am is 15 inches deep snow but what we have is 12 inches deep snow. The equation has failed in its prediction.

Step-by-step explanation:

In this question, we are asked to calculate if the prediction made by an equation modeled is correct.

Firstly let’s look at the equation in question;

y = 3t - 6

where y is the snow depth and t is the number of hours after midnight.

now we are looking at 7am, that’s 7 hours past 12am, meaning 7 hours after midnight.

let’s plug the value of t as 7 into the equation

y = 3(7) - 6

y = 21-6

y = 15 inches

according to the equation by Kevin, what is expected is 15 inches deep snow but what we have is 12 inches deep snow. The equation has failed in its prediction.

3 0
3 years ago
Given that the expression 2x^3 + mx^2 + nx + c leaves the same remainder when divided by x -2 or by x+1 I prove that m+n =-6
Alla [95]

Given:

The expression is:

2x^3+mx^2+nx+c

It leaves the same remainder when divided by x -2 or by x+1.

To prove:

m+n=-6

Solution:

Remainder theorem: If a polynomial P(x) is divided by (x-c), thent he remainder is P(c).

Let the given polynomial is:

P(x)=2x^3+mx^2+nx+c

It leaves the same remainder when divided by x -2 or by x+1. By using remainder theorem, we can say that

P(2)=P(-1)              ...(i)

Substituting x=-1 in the given polynomial.

P(-1)=2(-1)^3+m(-1)^2+n(-1)+c

P(-1)=-2+m-n+c

Substituting x=2 in the given polynomial.

P(2)=2(2)^3+m(2)^2+n(2)+c

P(2)=2(8)+m(4)+2n+c

P(2)=16+4m+2n+c

Now, substitute the values of P(2) and P(-1) in (i), we get

16+4m+2n+c=-2+m-n+c

16+4m+2n+c+2-m+n-c=0

18+3m+3n=0

3m+3n=-18

Divide both sides by 3.

\dfrac{3m+3n}{3}=\dfrac{-18}{3}

m+n=-6

Hence proved.

7 0
2 years ago
Crystal reads 25 pages in 1 hour. Write an equation to represent the 2
Inessa05 [86]

Answer:

she read 25 pages in 60 minutes

Step-by-step explanation:

8 0
3 years ago
1) A bag contains six red marbles and eight blue marbles. You randomly pick a marble and then pick a second marble without retur
Elena-2011 [213]

Answer:

You would have 4 red marbles and 8 blue marbles since you didn't return the ones you took out to the bag.

Step-by-step explanation:

6 - 2 = 4

The 8 would stay the same

There for you would have 4 red marbles and 8 blue marbles left in the bag. Totalled you have 12 marbles in the bag and 2 out of the bag. (8 + 4 = 12)

Including the marbles in and out of the bag you have 14 marbles. The 12 inside the bag + the 2 outside of the bag = 14 marbles totalled.

5 0
3 years ago
Find the length of AB if AC = 18 and BC = 7.
navik [9.2K]
I’m going to guess the the line is AC and B is the midpoint, if this is what ur asking this is ur answer
18-7
Answer
AB=11
5 0
2 years ago
Other questions:
  • Jon borrows 5.50 from his friends to pay for snacks, and 12.75 from his sister to go the movies. How much does he need to repay
    8·2 answers
  • Riverview Farms sold a combined total of 396 watermelons and cantaloupes. they sold 126 more watermelons than cantaloupes. Use n
    10·2 answers
  • Molly loves making chicken nuggets. She makes 4 1⁄2 servings. Molly
    14·1 answer
  • Point-Slope Form Practice
    12·1 answer
  • You deposit $200 in an account earning 2% interest compounded annually how much will you have any account in 10 years
    9·1 answer
  • WILL GIVE BRAINLIEST
    15·1 answer
  • Drag each measure to a box on the right to match the measure on the left. 5 feet10,560 feet48 inches126 inches 2 miles 123 yards
    7·1 answer
  • I’ve been stressing over this problem can anyone help how my answer would be 1
    6·2 answers
  • How many groups of 1 2/3 are in 4 1/3
    5·1 answer
  • 3. Jessie has 25 small
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!