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In the graph of this function why isn’t there a reflection across the origin Since there’s a negative before square root and also before x?

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Wdym mean across the origin? Note that sqrt() always returns a positive value so a negative in front of the square root means that y will always be below or equal to zero. If you are asking about the reflection in the y-axis, the negative sign in front if the x term does reflect the curve about the y-axis. Think about like this: you translate the curve 4 unites to the left, THEN you reflect the curve about the x axis, due to the negative sign. Of course the negative sign in front of the sqrt() reflects the curve in the x-axis. This will result in the curve you drew above, ignoring the dotted lines
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The reflection of sqrt(x-4) across the origin is -sqrt(-x-4).

This stuff is tricky! Cheers!
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f(x)=-sqrt(-1(x-4))

The negative inside reflects the sqrt(x-4) about the line x=4.

The negative outside reflects sqrt(4-x) across the x-axis.
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A reflection of what function across the origin? Please specify the function.

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