1. **Problem Statement:** Given the function $y = 4x^4 + 6$ with domain $x = \{-1,0,1,2,3\}$, we need to find the range values. 2. **Formula and Explanation:** The function is a polynomial where $y$ depends on $x$ raised to the fourth power, multiplied by 4, then increased by 6. 3. **Calculate Range Values:** - For $x = -1$: $y = 4(-1)^4 + 6 = 4(1) + 6 = 10$ - For $x = 0$: $y = 4(0)^4 + 6 = 0 + 6 = 6$ - For $x = 1$: $y = 4(1)^4 + 6 = 4(1) + 6 = 10$ - For $x = 2$: $y = 4(2)^4 + 6 = 4(16) + 6 = 64 + 6 = 70$ - For $x = 3$: $y = 4(3)^4 + 6 = 4(81) + 6 = 324 + 6 = 330$ 4. **Range Set:** The range values are $\{6, 10, 70, 330\}$. This completes the calculation of the range values for the given domain.