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What transformation can you apply to #y=sqrtx# to obtain the graph #y=3sqrt(-x)-4#?

Answer 1

Madelyn Anderson

Stretch by factor of #3#.
Reflect over y-axis.
Shift #4# units downward.

Multiplying by #3# stretches the graph by a factor of #3#.
Multiplying #x# by #-1# reflects the graph over the y-axis.
Subtracting #4# from the entire equation shifts the graph downwards #4# units.

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Answer 2

Serenity Jones

To transform the graph of ( y = \sqrt{x} ) to ( y = 3\sqrt{-x} - 4 ), you can follow these steps:

Reflect the graph of ( y = \sqrt{x} ) about the y-axis to account for the negative sign before the x under the square root.
Stretch the reflected graph vertically by a factor of 3, which will change the steepness of the graph.
Shift the stretched graph downward by 4 units to achieve the desired vertical shift.

The resulting graph will be ( y = 3\sqrt{-x} - 4 ).

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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.