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eduard
3 years ago
9

Which transfromations tranforms the graph of f(x)=x^2 to the graph of g(x)=(x+4)^2?

Mathematics
1 answer:
wariber [46]3 years ago
4 0

<em>Greetings from Brasil...</em>

In function F(X) = X², if we replace X with X + 4 we will have exactly function G(X) = (X + 4)²

So, just replace X for X + 4..... This will be responsible for translating 4 units to the left, because:

F(X) = X²

F(X + 4) = (X + 4)²

F(X + 4) ⇔ F(X + k)  <em>  see below</em>

We know that the translations are established as follows:

→ Horizontal

F(X + k) ⇒ k units to the left

F(X - k) ⇒ k units to the right

<em>see more:</em>

<em>brainly.com/question/17163323</em>

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-4r-11=4r+21 pls help <br>​
Masja [62]

-4r-11=4r+21

Move 4r to the other side

Sign changes from +4r to -4r

-4r-4r-11=4r-4r+21

-4r-4r-11=21

-8r-11=21

Move -11 to the other side

Sign changes from -11 to +11

-8r-11+11=21+11

-8r=21+11

-8r=32

Divide both sides by -8

-8r/-8=32/-8

Answer: r=-4

8 0
3 years ago
Read 2 more answers
What is the slope of the line that passes through (-3,4) and (-3,-4)
suter [353]

Answer:

undefined

Step-by-step explanation:

We can use the slope formula to find the slope

m = ( y2-y1)/(x2-x1)

    = ( -4-4)/( -3 - -3)

   = ( -4-4)/( -3+3)

   = -8/0

When we divide by zero, the answer is undefined so the slope is undefined

8 0
2 years ago
I get pretty confused with these types of questions ??
Evgen [1.6K]

this should help I have it step

5 0
3 years ago
Divide . Write the quotient as one power. The variable is not equal to zero.
gogolik [260]
I need the equation to be able to help
5 0
2 years ago
4TH TIME ASKING THIS!!! Please help me! Someone pleaseeee. I need the correct answers. I don’t want to fail
Alexeev081 [22]

Answer:

The functions are inverses; f(g(x)) = x ⇒ answer D

h^{-1}(x)=\sqrt{\frac{x+1}{3}} ⇒ answer D

Step-by-step explanation:

* <em>Lets explain how to find the inverse of a function</em>

- Let f(x) = y

- Exchange x and y

- Solve to find the new y

- The new y = f^{-1}(x)

* <em>Lets use these steps to solve the problems</em>

∵ f(x)=\sqrt{x-3}

∵ f(x) = y

∴ y=\sqrt{x-3}

- Exchange x and y

∴ x=\sqrt{y-3}

- Square the two sides

∴ x² = y - 3

- Add 3 to both sides

∴ x² + 3 = y

- Change y by f^{-1}(x)

∴ f^{-1}(x)=x^{2}+3

∵ g(x) = x² + 3

∴ f^{-1}(x)=g(x)

∴ <u><em>The functions are inverses to each other</em></u>

* <em>Now lets find f(g(x))</em>

- To find f(g(x)) substitute x in f(x) by g(x)

∵ f(x)=\sqrt{x-3}

∵ g(x) = x² + 3

∴ f(g(x))=\sqrt{(x^{2}+3)-3}=\sqrt{x^{2}+3-3}=\sqrt{x^{2}}=x

∴ <u><em>f(g(x)) = x</em></u>

∴ The functions are inverses; f(g(x)) = x

* <em>Lets find the inverse of h(x)</em>

∵ h(x) = 3x² - 1 where x ≥ 0

- Let h(x) = y

∴ y = 3x² - 1

- Exchange x and y

∴ x = 3y² - 1

- Add 1 to both sides

∴ x + 1 = 3y²

- Divide both sides by 3

∴ \frac{x + 1}{3}=y^{2}

- Take √ for both sides

∴ ± \sqrt{\frac{x+1}{3}}=y

∵ x ≥ 0

∴ We will chose the positive value of the square root

∴ \sqrt{\frac{x+1}{3}}=y

- replace y by h^{-1}(x)

∴ h^{-1}(x)=\sqrt{\frac{x+1}{3}}

4 0
3 years ago
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