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Sauron [17]
3 years ago
12

Write an equation for the translation of the function. y = cos x; translated 6 units up

Mathematics
2 answers:
Yakvenalex [24]3 years ago
6 0
It's just y= cos(x)+6
nlexa [21]3 years ago
5 0

Answer:

y=cos(x)+6.

Step-by-step explanation:

We are asked to write an equation for the translation of the function y=cos(x) to 6 units upwards.

Let us recall transformation rules.

f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}

f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}

f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}

f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}

Since we need to shift our given function 6 units upwards, so we will add 6 to our given function outside the parenthesis as:

y=cos(x)+6

Therefore, our required equation would be y=cos(x)+6.

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Manuela solved the equation 3−2|0.5x+1.5|=2 for one solution. Her work is shown below. 3−2|0.5x+1.5|=2 −2|0.5x+1.5|=−1 |0.5x+1.5
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Answer:

x=-4

Step-by-step explanation:

The given equation is

3-2|0.5x+1.5|=2

Subtract 3 from both sides.

3-2|0.5x+1.5|-3=2-3

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Divide both sides by -2.

\dfrac{-2|0.5x+1.5|}{-2}=\dfrac{-1}{-2}

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If |x|=a, then x=a or x=-a.

0.5x+1.5=\pm 0.5

Case 1: 0.5x+1.5=0.5

Subtract 1.5 from both sides.

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Divide both sides by 0.5.

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Case 2: 0.5x+1.5=-0.5

Subtract 1.5 from both sides.

0.5x=-0.5-1.5

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Divide both sides by 0.5.

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Step-by-step explanation:

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