# How do you describe the transformation of #f(x)=sqrt(1/2x)-4# from a common function that occurs and sketch the graph?

We can write the given equation:

In the form:

We should now recognise this as the graph of the function

graph{sqrt(x) [-5, 10, -8, 8]}

Which is:

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The function (f(x) = \sqrt{\frac{1}{2}x} - 4) can be described as a transformation of the square root function. The transformation involves a horizontal compression by a factor of 2, a reflection about the y-axis, and a vertical translation downward by 4 units.

To sketch the graph, start with the basic square root function (y = \sqrt{x}). Apply the transformations:

- Horizontal compression by a factor of 2: This makes the graph wider. Points on the graph move closer to the y-axis.
- Reflection about the y-axis: This flips the graph to the left side of the y-axis.
- Vertical translation downward by 4 units: This shifts the entire graph downward by 4 units.

Plotting these transformations on the graph of the square root function will give you the graph of (f(x)).

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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.

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