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Question Find the mapping rule for the function y=2−(x+3)−4y=2 \sqrt{-(x+3)}-4.

Studdy Solution

STEP 1

Assumptions1. The given function is y=−(x+3)−4y= \sqrt{-(x+3)}-4 . We need to determine the mapping rule for this function

STEP 2

The mapping rule for a function describes how each input (or 'x' value) is transformed into the corresponding output (or 'y' value).For our function y=2−(x+)−4y=2 \sqrt{-(x+)}-4, we can see that the input 'x' undergoes several transformations1. It is first added by2. The result is then negated. The square root of the result is taken4. The result is then multiplied by25. Finally,4 is subtracted from the result

STEP 3

We can express these transformations as a sequence of operations on 'x', which gives us the mapping rule1. x→x+3x \rightarrow x+3
2. x+3→−(x+3)x+3 \rightarrow -(x+3)3. −(x+3)→−(x+3)-(x+3) \rightarrow \sqrt{-(x+3)} . −(x+3)→2−(x+3)\sqrt{-(x+3)} \rightarrow2\sqrt{-(x+3)}
5. 2−(x+3)→2−(x+3)−2\sqrt{-(x+3)} \rightarrow2\sqrt{-(x+3)}-
So, the mapping rule for the function y=2−(x+3)−y=2 \sqrt{-(x+3)}- isx→x+3→−(x+3)→−(x+3)→2−(x+3)→2−(x+3)−x \rightarrow x+3 \rightarrow -(x+3) \rightarrow \sqrt{-(x+3)} \rightarrow2\sqrt{-(x+3)} \rightarrow2\sqrt{-(x+3)}-

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