1. **State the problem:** Find the range of the function $$y=\sqrt{5x+4}$$ for the domain values given. 2. **Identify the domain:** The problem gives multiple domain options, but the first domain mentioned is from 0 to 1. 3. **Recall the range definition:** The range is the set of all possible output values (y-values) of the function for the given domain. 4. **Evaluate the function at the domain endpoints:** - At $$x=0$$: $$y=\sqrt{5(0)+4}=\sqrt{4}=2$$ - At $$x=1$$: $$y=\sqrt{5(1)+4}=\sqrt{9}=3$$ 5. **Determine the range:** Since the square root function is increasing, the range for $$x \in [0,1]$$ is $$[2,3]$$. 6. **Check other domain options:** The problem lists other domain pairs, but since the first domain is 0 to 1, the range is $$2$$ to $$3$$. **Final answer:** The range of $$y=\sqrt{5x+4}$$ for $$x \in [0,1]$$ is $$[2,3]$$.