F(x) = x^2. What is g(x)

F(x) = X^2. What Is G(x)

Answers

Answer 1

Answer:

g(x) = - x² - 4 ⇒ A

Step-by-step explanation:

Let us revise the reflection and translation of a function

If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)  If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)  If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k  If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) – k  

f(x) = x² is the blue curve

g(x) is its image is the red curve

∵ g(x) is the image of f(x)

∵ f(x) is opened upward

∵ g(x) is opened downward

→ That means the sign of y-coordinates of all points on the blue

   graph are opposite

f(x) is reflected about the x-axis

Its image is - f(x)

∵ The vertex of f(x) is (0, 0)

∵ The vertex of g(x) = (0, -4)

→ That means the function translated 4 units down

- f(x) is translated 4 units down

Its image is - f(x) - 4

∴ g(x) = - f(x) - 4

∵ f(x) = x²

g(x) = - x² - 4


Related Questions

How can i use multiplication/division to calculate a percent of a number?

Answers

Answer:

for example you are given a percentage and numbers you cross multiply

Step-by-step explanation:

hope it helps cause I don't know how to explain the answer

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he can make 4 stacks, leaving 8 chairs as single chairs

What are the zeros of x (3 - 18x) = 0 ?

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Answer:

x=3⋅±  2

​  

=±4.2426

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Step-by-step explanation:

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The answer would be 10 1/2

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Find one counterexample to show that each conjecture is false.

Answers

Answer:

make each of the supplementary angles 90, then they are equal.                                                                                                                                                                                                                                                                                                                  

Step-by-step explanation:

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c

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KN

Answers

Step-by-step explanation:

The sum of interior angles of a triangle is 180 degree

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The sum of three consecutive integers is 42. Determine the value of the smallest
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Answers

Answer:

13.

Step-by-step explanation:

[tex]42 = a + (a+1) + (a+2) = 3a + 3 = 3(a+1)[/tex]

Then, [tex]a+1 = 14[/tex], so [tex]a=13.[/tex]

Please help on this I’m confused

Answers

Answer:

Side A is 7

Side B is 15

Step-by-step explanation:

$182 at 6% simple interest for 4 years.
Find the interest earned on the account​

Answers

The interest is $43.68

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Answers

$$$$$$$$$$$$$$$$$$$$$$$$$$

This situation can be represented by y=.10x+.50
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A dance floor is in the shape of a rectangle.
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Answers

Answer:

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Step-by-step explanation:

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Allisa needs a new fish tank. Her new fish tank must hold 175% of the water that her old one holds. The old fish tank holds 20 gallons of water. How many gallons of water should her new fish tank hold? O A. A. 15 gallons B. 35 gallons OC. 60 gallons D. 80 gallons E. 95 gallons​

Answers

Answer:

b

Step-by-step explanation:

75 percent of 20 is 15 and 100 percent of 20 is 20

The number of gallons of water should her new fish tank hold is to be considered as the option b. 35 gallons.

Calculation of the number of gallons:

Since

Allisa needs a new fish tank. Her new fish tank must hold 175% of the water that her old one holds.

The old fish tank holds 20 gallons of water.

So we can say that

= 75% of 20 + 100% of 20

= 15 + 20

= 35

Hence, the option b is correct.

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Answers

Answer:

1. True

2. False

3. True

4. False

5. True

Step-by-step explanation:

For 1, you want to see the reduced fraction of 2/6 so you want to divide 2/6 by 2, it is 1/3 and 2/3 is greater than 1/3.

For 2, you want to multiply 5 by 2. and then do the same thing for 6, 6 x 2. Now you want to see if they match.

For 3, you want to make both fractions into decimals so 1/8 is 0.125 and 1/4 is 0.25 and see which is larger.

For 4, you want to see if you can simplify any of them. 2/4 can be simplifed to 1/2. So, it is false because you can see that 2/4 is the same as 1/2

For 5, you want to divide both fractions by 2, so 4/10 would be 2/5 and 4/6 would be 2/3. So it is true.

The answers for the given expressions are given below,

1. True

2. False

3. True

4. False

5. True

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

For 1, you want to see the reduced fraction of 2/6 so you want to divide 2/6 by 2, it is 1/3, and 2/3 is greater than 1/3.

For 2, you want to multiply 5 by 2. and then do the same thing for 6, 6 x 2. Now you want to see if they match.

For 3, you want to make both fractions into decimals so 1/8 is 0.125 and 1/4 is 0.25, and see which is larger.

For 4, you want to see if you can simplify any of them. 2/4 can be simplified to 1/2. So, it is false because you can see that 2/4 is the same as 1/2

For 5, you want to divide both fractions by 2, so 4/10 would be 2/5, and 4/6 would be 2/3. So it is true.

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#SPJ2

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Answers

The most common formula for average speed is distance traveled divided by time taken. The other formula, if you have the initial and final speed, add the two together, and divide by 2

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Que paso que soaso por que yo no le tiendo que paso que paiooo por qhejbocjnsuwojrfnoedorjdowxxexisxecejxiwxbfuwbduwbxuwjuxbwxuwbdiwbxiwnixwnfinfiwndinwdinwidnwixjwixjiwnxiwnfiixwnxiwnxiw
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in
5 in
B in
4 in

Answers

Answer:

48 in²

Step-by-step explanation:

A1 = 9 x 4 = 36

A1 = 4 x 3 = 12

Total = 36 + 12

        = 48 in²

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Answers

Answer:

A

Step-by-step explanation:

Zeke's birthday party will cost $6 if he invites 3 guests. If there are 8 guests,
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Answers

If Zeke invites 8 guests, his party will cost $16. Its $2 per guest

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Answer:

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Step-by-step explanation:

If the expression 4x+3 is equal to 1 to the same value of x, what is the expression 4x+8 equal to for the same value of x?

Answers

Answer:

6

Step-by-step explanation:

4x + 3 = 1

4x =-2

x = -1/2 so 4x +8 =4(-1/2) +8=6

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Answers

Answer:

You must first put the equation into slope-intercept form (y = mx + b). To do this, subtract x from both sides to isolate y. Then, since y will be negative, divide each side by -1, resulting in y = x - 3. Since a 1 is understood to be in front of the x, the slope is 1

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x- 3 y-0 or (3,0)

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Answers

(12,1) would be the new points so count from there!

How do you do this question?

Answers

4 Answers: A, B, C, D

=======================================================

Explanation:

f(x) is continuous when x >= 1. The only discontinuity for f(x) is when x = 0, but 0 is not part of this interval.

f(x) is positive for any valid x value in the domain since x^6 is always positive. In general, x^n is positive for all x when n is any even number.

f(x) is decreasing. You can see this through a table of values or through a graph. For anything in the form 1/(x^k), it will be a decreasing function because x^k gets larger, so 1/(x^k) gets smaller, when x goes to infinity.

--------------------

The conditions to use the integral test have been met. So we have to see if [tex]\displaystyle \int_1^{\infty}f(x)dx[/tex] converges or not.

Let's integrate and find out

[tex]\displaystyle \int \frac{1}{x^6} dx = \int x^{-6} dx\\\\\\ \displaystyle \int \frac{1}{x^6} dx = \frac{1}{1+(-6)}x^{-6+1}+C\\\\\\ \displaystyle \int \frac{1}{x^6} dx = \frac{1}{-5}x^{-5}+C\\\\\\ \displaystyle \int \frac{1}{x^6} dx = -\frac{1}{5}*\frac{1}{x^5}+C\\\\\\ \displaystyle \int \frac{1}{x^6} dx = -\frac{1}{5x^5}+C\\\\[/tex]

So we have

[tex]\displaystyle g(x) = \int f(x) dx\\\\\\\displaystyle g(x) = \int \frac{1}{x^6} dx\\\\\\\displaystyle g(x) = -\frac{1}{5x^5}+C\\\\\\[/tex]

Meaning that,

[tex]\displaystyle \int_{a}^{b} f(x) dx = g(b)-g(a)\\\\\\\displaystyle \int_{a}^{b} \frac{1}{x^6} dx = \left(-\frac{1}{5b^5}+C\right)-\left(-\frac{1}{5a^5}+C\right)\\\\\\\displaystyle \int_{a}^{b} \frac{1}{x^6} dx = -\frac{1}{5b^5}+\frac{1}{5a^5}\\\\\\[/tex]

If we plug in a = 1 and apply the limit as b approaches positive infinity, then the expression [tex]-\frac{1}{5b^5}+\frac{1}{5a^5}[/tex] will turn into [tex]\frac{1}{5}[/tex]

Therefore,

[tex]\displaystyle \int_{1}^{\infty} \frac{1}{x^6} dx = \frac{1}{5}\\\\\\[/tex]

Because this integral converges, this means the series [tex]\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^6}[/tex] also converges as well by the integral test.

• Number of psychology textbooks sold: The number is not correct
A textbook store sold a combined total of 334 biology and psychology textbooks in a week. The number of biology textbooks sold was 84 more than the number
of psychology textbooks sold. How many textbooks of each type were sold?

Answers

Answer:

209 biology books and 125 psychology books were sold.

Step-by-step explanation:

x = biology books y = psychology books

334 = x + y

x = y + 84

x - y = 84

y = x - 84

Using these systems of equations, we can see that (209,125) is the only possible answer. Elimination, substitution, or guess and check are all viable methods to solve this problem. I can explain further if needed! :)

While I was walking to schoed this morning I saw 2 ants and 2 butterflies.
My teacher taught me that an insect has 6 legs. Ants one butterflies are
both intects! How many legs were there all together?

Answers

Answer:

it would me 24 legs

Step-by-step explanation:

hope that helps

They are 24 legs in total

please gyus help me out ..... urgent need......for 20 points please gyus answer it .....​

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Answer:

I wish I could help you but i have not learn yhat yet. so sorrry :( pleaser forgive jme....... please i beg u plase

Step-by-step explanation:

what do you mean by '^' next to everything?

Answers

Answer:

power of for example 4 to the power of 2. 2 means square

Which of the following functions is graphed below?

Answers

The second answer, B
It’s the second one It’s b

Beck uses 25 robux to buy 3 spins on a game she likes, she spends 8 thousand robux to finally roll a good item.How much spins did she get?

Answers

Answer:

960

Step-by-step explanation:

8000/25 = 320

320 • 3 = 960

The answer is 960 :)
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