# How do you describe the transformation of #f(x)=2-(x+5)^2# from a common function that occurs and sketch the graph?

This way.

Hence, we get the required graph.

graph{2- (x+5)^2 [-10, 10, -5, 5]}

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The transformation of (f(x) = 2 - (x + 5)^2) involves a vertical translation of 2 units upwards and a horizontal translation of 5 units to the left compared to the parent function (f(x) = -x^2). The negative sign inside the parentheses reflects the reflection about the y-axis.

To sketch the graph:

- Start with the graph of the parent function (f(x) = -x^2).
- Shift the graph 5 units to the left to account for the horizontal translation.
- Then, shift the graph 2 units upwards to account for the vertical translation.
- The graph will open downwards due to the negative sign associated with the quadratic term.

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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.

- What is the transformations needed to obtain #2x^3# from the graph of #x^3#?
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- How do you find the vertical, horizontal and slant asymptotes of: #f(x) = (2x-1) / (x - 2)#?
- How do you determine if #f(x) = x^3 - x^5# is an even or odd function?
- What transformation can you apply to #y=sqrtx# to obtain the graph #y=sqrt(-2x)-8#?

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