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Studentka2010 [4]
2 years ago
7

If f(x) = |x| and g(x) = |x| − 4, which translation is applied to f(x) to get g(x)? A. a vertical translation of f(x) four units

upward B. a horizontal translation of f(x) four units to the left C. a horizontal translation of f(x) four units to the right D. a vertical translation of f(x) four units downward
Mathematics
1 answer:
Sav [38]2 years ago
3 0

Hey there! :)

Answer:

D. A vertical translation of f(x) four units downward.

Step-by-step explanation:

Recall that the transformations form of an absolute value function is:

f(x) = ±a|b(x-h)|+k

Where 'a' is a vertical stretch/compression

'b' is a horizontal stretch/compression

'h' is a horizontal shift

'k' is a vertical shift

In g(x) = |x| -4, we can derive a k value of -4.

This means that from f(x) to g(x), there has been a vertical translation of f(x) four units downward.

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N76 [4]

To start to solve this problem, we need to know what vertex form is. The vertex form of a parabola is. The vertex form of a parabola is a(x-h) + k, where k is the vertical shift, h is the horizontal shift, and a is the value that tells the stretch.


To start to solve this equation, we want to start to create a difference of two squares.

y = 2(x²+\frac{1}{2}x) We do this step to make the x² have a coefficient of 1

Now, we want to complete the square. To complete the square, we take 1/2 of the coefficient of x, and then square that.

1/2 * 1/2 = 1/4, and 1/4²=1/16

That means that we need to add 1/16 inside and outside the parenthesis.

We get:

y = 2(x²+1/2x + 1/16) - 1/16*2

We do -1/16*2 on the outside because since we added it inside the parenthesis, we need to take it away somewhere else (if that makes sense). The two is there because there is a two in front of the parenthesis.

We get:

y = 2(x+1/4)² - 1/8, by completing the square and simplifying, and this is the final answer.



4 0
2 years ago
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Find the product <br><br> 5/6 * 30
olga55 [171]
25

Explanation:

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Because 30 is a whole number one puts it over 1 and since it’s multiplication one multiplies straight across

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2 years ago
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Basile [38]

Answer:

<h2>\boxed{\bold{x \ = \ 2}}</h2>

Explanation:

3(x + 6) = 24

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3(x + 6) = 24

(3)(x) + (3)(6) = 24 (Distribute)

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3x + 18 − 18 = 24 − 18

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2 years ago
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Step-by-step explanation:

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4 0
2 years ago
(01.01) Kisha and Rae are asked to solve −5x − 14 = 2x + 7. Identify where one of them made an error.
lora16 [44]
It's A. 
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