# How do you describe the transformation of #f(x)=sqrt(x+4)+8# from a common function that occurs and sketch the graph?

The 8 shifts the graph up 8 and the 4 shifts the graph left 4.

The parent function is:

There is a number inside the square root and a number outside the square root that is being added to this function.

The number on the inside always shifts it in the x direction. If the number is positive, it shifts the graph to the left and if the number is negative, it shifts the graph to the right.

Since our number is a positive 4, it will shift our graph to the left 4 spaces.

The number being added will always shift it in the y direction. If the number is positive, it shifts the graph up and if the number is negative, it shifts the graph down.

Since our number is a positive 8, it will shift our graph up 8 spaces.

When graphing it, our curve takes on a square root shape since our parent function is a square root function:

graph{sqrt(x+4)+8 [-8.4, 14.11, 5.025, 16.265]}

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The function ( f(x) = \sqrt{x+4} + 8 ) is a transformation of the basic square root function ( f(x) = \sqrt{x} ).

- Horizontal Translation: The function ( \sqrt{x+4} ) is a horizontal shift of the basic square root function to the left by 4 units.
- Vertical Translation: Adding 8 to ( \sqrt{x+4} ) shifts the graph vertically upward by 8 units.

To sketch the graph:

- Start with the basic square root function ( y = \sqrt{x} ).
- Apply a horizontal shift of 4 units to the left, which moves the graph to the left.
- Then, apply a vertical shift of 8 units upward to the graph.
- Plot key points to accurately represent the shape of the transformed graph.
- Draw the transformed graph, ensuring it maintains the characteristic shape of a square root function, but shifted horizontally and vertically as described.

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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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