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What kind of transformation converts the graph of f(x)=−4(x+2)2+6f(x) = -4(x + 2)^2 + 6 into the graph of g(x)=−4(x−2)2+6g(x) = -4(x - 2)^2 + 6?\newlineChoices:\newline(A) translation 44 units left\newline(B) translation 44 units down\newline(C) translation 44 units up\newline(D) translation 44 units right

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Describe function transformationsright chevron icon

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Rakesh tried to solve the differential equation dydx=2y⋅cos⁡(x) \frac{d y}{d x}=2 y \cdot \cos (x) . This is his work:\newlinedydx=2y⋅cos⁡(x) \frac{d y}{d x}=2 y \cdot \cos (x) \newlineStep 11: ∫1ydy=∫2cos⁡(x)dx \quad \int \frac{1}{y} d y=\int 2 \cos (x) d x \newlineStep 22: ln⁡∣y∣=2sin⁡(x) \quad \ln |y|=2 \sin (x) \newlineStep 33: eln⁡∣y∣=e2sin⁡(x) \quad e^{\ln |y|}=e^{2 \sin (x)} \newlineStep 44: ∣y∣=e2sin⁡(x) \quad|y|=e^{2 \sin (x)} \newlineStep 55: y=±e2sin⁡(x)+C \quad y= \pm e^{2 \sin (x)}+C \newlineIs Rakesh's work correct? If not, what is his mistake?\newlineChoose 11 answer:\newline(A) Rakesh's work is correct.\newline(B) Step 11 is incorrect. The separation of variables wasn't done correctly.\newline(C) Step 22 is incorrect. The right-hand side of the equation should be 2sin⁡(x)+C 2 \sin (x)+C .\newline(D) Step 44 is incorrect. eln⁡∣y∣ e^{\ln |y|} isn't equal to ∣y∣ |y| .
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Posted 9 months ago

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What kind of transformation converts the graph of f(x)=−8(x+5)2−10f(x) = -8(x + 5)^2 - 10 into the graph of g(x)=−8(x+4)2−10g(x) = -8(x + 4)^2 - 10?\newlineChoices:\newline(A) translation 11 unit up\newline(B) translation 11 unit left\newline(C) translation 11 unit right\newline(D) translation 11 unit down
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Posted 8 months ago

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What kind of transformation converts the graph of f(x)=(x+7)2+3f(x) = (x + 7)^2 + 3 into the graph of g(x)=(x+7)2+1g(x) = (x + 7)^2 + 1?\newlineChoices:\newline(A) translation 22 units up\newline(B) translation 22 units left\newline(C) translation 22 units down\newline(D) translation 22 units right
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Posted 8 months ago

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What kind of transformation converts the graph of f(x)=4∣x−5∣+9f(x) = 4|x - 5| + 9 into the graph of g(x)=4∣x−6∣+9g(x) = 4|x - 6| + 9?\newlineChoices:\newline(A) translation 11 unit up\newline(B) translation 11 unit down\newline(C) translation 11 unit right\newline(D) translation 11 unit left
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Posted 8 months ago

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What kind of transformation converts the graph of f(x)=−9∣x−7∣+4f(x) = -9|x - 7| + 4 into the graph of g(x)=−9∣x−7∣+8g(x) = -9|x - 7| + 8?\newlineChoices:\newline(A) translation 44 units down\newline(B) translation 44 units right\newline(C) translation 44 units left\newline(D) translation 44 units up
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Posted 8 months ago

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What kind of transformation converts the graph of f(x)=6(x+2)2+2f(x) = 6(x + 2)^2 + 2 into the graph of g(x)=6(x+3)2+2g(x) = 6(x + 3)^2 + 2?\newlineChoices:\newline(A) translation 11 unit left\newline(B) translation 11 unit right\newline(C) translation 11 unit down\newline(D) translation 11 unit up
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Posted 8 months ago

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What kind of transformation converts the graph of f(x)=−4∣x−7∣+10f(x) = -4|x - 7| + 10 into the graph of g(x)=−4∣x−8∣+10g(x) = -4|x - 8| + 10?\newlineChoices:\newline(A) translation 11 unit left\newline(B) translation 11 unit down\newline(C) translation 11 unit right\newline(D) translation 11 unit up
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Posted 8 months ago

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What kind of transformation converts the graph of f(x)=−7(x−9)2f(x) = -7(x - 9)^2 into the graph of g(x)=−7(x−9)2−5g(x) = -7(x - 9)^2 - 5?\newlineChoices:\newline(A) translation 55 units up\newline(B) translation 55 units right\newline(C) translation 55 units down\newline(D) translation 55 units left
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Posted 8 months ago

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What kind of transformation converts the graph of f(x)=8(x+3)2−4f(x) = 8(x + 3)^2 - 4 into the graph of g(x)=8(x+3)2−8g(x) = 8(x + 3)^2 - 8?\newlineChoices:\newline(A) translation 44 units right\newline(B) translation 44 units left\newline(C) translation 44 units down\newline(D) translation 44 units up
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Posted 8 months ago

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What kind of transformation converts the graph of f(x)=−10∣x+6∣−5f(x) = -10|x + 6| - 5 into the graph of g(x)=−10∣x+6∣+3g(x) = -10|x + 6| + 3?\newlineChoices:\newline(A) translation 88 units right\newline(B) translation 88 units down\newline(C) translation 88 units left\newline(D) translation 88 units up
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Posted 8 months ago

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