Question 8
The set of all $x$-coordinates of points on the curve $y=\sqrt{4-x}$ is described by:
\(\boxed{x \leq 4}\) is the final answer.
Step 1 :The function \(y=\sqrt{4-x}\) is defined for all \(x\) such that \(4-x \geq 0\). This is because the square root of a negative number is not a real number.
Step 2 :Therefore, we need to solve the inequality \(4-x \geq 0\) to find the set of all \(x\)-coordinates of points on the curve.
Step 3 :The solution to the inequality \(4-x \geq 0\) is \(x \leq 4\).
Step 4 :This means that the set of all \(x\)-coordinates of points on the curve \(y=\sqrt{4-x}\) is all real numbers less than or equal to 4.
Step 5 :\(\boxed{x \leq 4}\) is the final answer.