Let \( g \) be the function from \( S=\{0,1,2,3,4\} \) to the whole numbers \( W \) given by the formula \( g(x)=7-2 x+x^{2} \). (a) Find \( g(0), g(1), g(2), g(3) \), and \( g(4) \). (b) What is the range of \( g \) ? (a) \( g(0)=\square \)

To evaluate the function \( g(x) = 7 - 2x + x^2 \) for the given values: (a) 1. \( g(0) = 7 - 2(0) + (0)^2 = 7 \) 2. \( g(1) = 7 - 2(1) + (1)^2 = 7 - 2 + 1 = 6 \) 3. \( g(2) = 7 - 2(2) + (2)^2 = 7 - 4 + 4 = 7 \) 4. \( g(3) = 7 - 2(3) + (3)^2 = 7 - 6 + 9 = 10 \) 5. \( g(4) = 7 - 2(4) + (4)^2 = 7 - 8 + 16 = 15 \) So, the values are: \( g(0) = 7 \) \( g(1) = 6 \) \( g(2) = 7 \) \( g(3) = 10 \) \( g(4) = 15 \) (b) The range of \( g \) is the set of distinct outputs from the values calculated: \[ \text{Range of } g = \{6, 7, 10, 15\} \]