Sure! Let's decipher the function machine based on the given information. The machine takes an input [tex]\(x\)[/tex] and processes it to produce an output.
The rule for this function machine is described by the equation:
[tex]\[ \text{Output} = 6x + 47 \][/tex]
Let's break down the equation:
1. Input: The input to the function machine is denoted by [tex]\(x\)[/tex].
2. Processing Rule: Each input [tex]\(x\)[/tex] is multiplied by 6.
3. Addition: After multiplying by 6, we add 47 to the result.
Therefore, the equation that represents the function machine is:
[tex]\[ \text{Output} = 6x + 47 \][/tex]
To visualize this with examples:
- If the input [tex]\(x = 1\)[/tex]:
[tex]\[ \text{Output} = 6(1) + 47 = 6 + 47 = 53 \][/tex]
- If the input [tex]\(x = 2\)[/tex]:
[tex]\[ \text{Output} = 6(2) + 47 = 12 + 47 = 59 \][/tex]
- If the input [tex]\(x = 5\)[/tex]:
[tex]\[ \text{Output} = 6(5) + 47 = 30 + 47 = 77 \][/tex]
Thus, the general form of the equation for the function machine is:
[tex]\[ \boxed{6x + 47} \][/tex]
This equation succinctly captures the relationship between the input [tex]\(x\)[/tex] and the output produced by the function machine.
