$$ 1 \leftarrow \quad $$ 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) $$ g(0)=7, g(1)=\square $$

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Evaluate the expression by following steps:
- step0: Evaluate:
  $$7-2x+x^{2}$$
- step1: Substitute:
  $$7-2\times 4+4^{2}$$
- step2: Multiply the numbers:
  $$7-8+4^{2}$$
- step3: Evaluate the power:
  $$7-8+16$$
- step4: Calculate:
  $$15$$
Substitute $$ x=1 $$ into the expression $$ 7-2x+x^2 $$.
Evaluate the expression by following steps:
- step0: Evaluate:
  $$7-2x+x^{2}$$
- step1: Substitute:
  $$7-2\times 1+1^{2}$$
- step2: Evaluate the power:
  $$7-2\times 1+1$$
- step3: Multiply:
  $$7-2+1$$
- step4: Calculate:
  $$6$$
Substitute $$ x=0 $$ into the expression $$ 7-2x+x^2 $$.
Evaluate the expression by following steps:
- step0: Evaluate:
  $$7-2x+x^{2}$$
- step1: Substitute:
  $$7-2\times 0+0^{2}$$
- step2: Calculate:
  $$7-2\times 0+0$$
- step3: Multiply:
  $$7+0+0$$
- step4: Remove 0:
  $$7$$
Substitute $$ x=2 $$ into the expression $$ 7-2x+x^2 $$.
Evaluate the expression by following steps:
- step0: Evaluate:
  $$7-2x+x^{2}$$
- step1: Substitute:
  $$7-2\times 2+2^{2}$$
- step2: Multiply the numbers:
  $$7-4+2^{2}$$
- step3: Evaluate the power:
  $$7-4+4$$
- step4: Calculate:
  $$7$$
Substitute $$ x=3 $$ into the expression $$ 7-2x+x^2 $$.
Evaluate the expression by following steps:
- step0: Evaluate:
  $$7-2x+x^{2}$$
- step1: Substitute:
  $$7-2\times 3+3^{2}$$
- step2: Multiply the numbers:
  $$7-6+3^{2}$$
- step3: Evaluate the power:
  $$7-6+9$$
- step4: Calculate:
  $$10$$
Let's solve the problem step by step.

### Part (a)
We need to evaluate the function $$ g(x) = 7 - 2x + x^2 $$ for $$ x = 0, 1, 2, 3, 4 $$.

1. **For $$ g(0) $$**:
   $$
   g(0) = 7 - 2(0) + (0)^2 = 7
   $$

2. **For $$ g(1) $$**:
   $$
   g(1) = 7 - 2(1) + (1)^2 = 7 - 2 + 1 = 6
   $$

3. **For $$ g(2) $$**:
   $$
   g(2) = 7 - 2(2) + (2)^2 = 7 - 4 + 4 = 7
   $$

4. **For $$ g(3) $$**:
   $$
   g(3) = 7 - 2(3) + (3)^2 = 7 - 6 + 9 = 10
   $$

5. **For $$ g(4) $$**:
   $$
   g(4) = 7 - 2(4) + (4)^2 = 7 - 8 + 16 = 15
   $$

Thus, we have:
- $$ g(0) = 7 $$
- $$ g(1) = 6 $$
- $$ g(2) = 7 $$
- $$ g(3) = 10 $$
- $$ g(4) = 15 $$

### Part (b)
Now, let's find the range of $$ g $$. The values we calculated are:
- $$ g(0) = 7 $$
- $$ g(1) = 6 $$
- $$ g(2) = 7 $$
- $$ g(3) = 10 $$
- $$ g(4) = 15 $$

The unique values are $$ 6, 7, 10, 15 $$.

Therefore, the range of $$ g $$ is:
$$
\text{Range of } g = \{6, 7, 10, 15\}
$$
(a) $$ g(0) = 7 $$, $$ g(1) = 6 $$, $$ g(2) = 7 $$, $$ g(3) = 10 $$, $$ g(4) = 15 $$ (b) The range of $$ g $$ is $$ \{6, 7, 10, 15\} $$.

\( 1 \leftarrow \quad \) 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) \( g(0)=7, g(1)=\square \)

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