Questions: Determine the restricted domain of the function r(x)=-√(-2x-80)

Transcript text: Determine the restricted domain of the function $r(x)=-\sqrt{-2 x-80}$

Solution

Solution Steps

Step 1: Identify the highest and lowest y-values

The highest y-value of the graph is 3. The lowest y-value of the graph approaches negative infinity.

Step 2: Express the range in inequality notation

Since the graph reaches a maximum y-value of 3 and extends downwards to negative infinity, the range can be represented as $y \le 3$.

Step 3: Determine the values allowed under the square root

We are not allowed to have negative values under the square root sign. Thus, the expression under the square root must be greater than or equal to zero: $-2x - 80 \ge 0$.

Step 4: Solve the inequality

Add 80 to both sides: $-2x \ge 80$. Divide both sides by -2 and remember to flip the inequality sign: $x \le -40$.

Final Answer

$ \boxed{y \le 3} $
$ \boxed{x \le -40} $

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