How do you identify the transformation of #h(x)=-2sqrt(x-4)#?
graph{y = sqrtx}
graph{y = sqrt(x-4}
graph{y = 2sqrt(x-4)}
graph{y=-2sqrt(x-4)}
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The function ( h(x) = -2\sqrt{x-4} ) represents a transformation of the square root function ( \sqrt{x} ). Specifically, it involves the following transformations:
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Horizontal Translation: The function is shifted 4 units to the right compared to the parent function ( \sqrt{x} ) due to the term ( x - 4 ) inside the square root.
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Vertical Stretch/Compression: The function is vertically stretched/compressed by a factor of 2 compared to the parent function ( \sqrt{x} ) due to the coefficient -2.
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Reflection: The function is reflected about the x-axis due to the negative sign before the square root.
Overall, the transformation involves a horizontal translation, a vertical stretch/compression, and a reflection about the x-axis.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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