How do you identify the transformation of #h(x)=-2sqrt(x-4)#?

Answer 1
Let's look at the parent function, #y = sqrtx#

graph{y = sqrtx}

Now let's shift it to the right by #4# to give us #y = sqrt (x-4)#

graph{y = sqrt(x-4}

Now we can stretch the graph by a factor of #2# by multiplying the equation by #2#: #y = 2sqrt(x-4)#

graph{y = 2sqrt(x-4)}

And now we deal with the negative sign. This flips the graph across the #x#-axis

graph{y=-2sqrt(x-4)}

There we go! We took the parent graph, #sqrt(x)# and shifted it to the right #4# units, then we stretched the graph by a factor of #2#, and finally we flipped the graph across the #x#-axis.
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Answer 2

The function ( h(x) = -2\sqrt{x-4} ) represents a transformation of the square root function ( \sqrt{x} ). Specifically, it involves the following transformations:

  1. 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.

  2. 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.

  3. 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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Answer from HIX Tutor

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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