What would the output be, if the input of this function machine was 1?Can you see that to find the output you would calculate 1 x 2 + 3 and you would get 
?
?What is the output if the input is 2?Can you see that the output is 2 x 2 + 3 which is 
?
?What if the input is 10?Can you see that the output is 10 x 2 + 3 which is 
?
?

To solve the problem, we need to determine the output of a function machine for given inputs using the given rule: \( \text{Output} = \text{Input} \times 2 + 3 \).

Let's calculate the outputs for the specified inputs:

### Step-by-Step Calculations:

1. **Input: 1**
   \[
   \text{Output} = 1 \times 2 + 3 = 2 + 3 = 5
   \]

2. **Input: 2**
   \[
   \text{Output} = 2 \times 2 + 3 = 4 + 3 = 7
   \]

3. **Input: 10**
   \[
   \text{Output} = 10 \times 2 + 3 = 20 + 3 = 23
   \]

### Summary of Outputs:
- For input \( 1 \), the output is \( 5 \).
- For input \( 2 \), the output is \( 7 \).
- For input \( 10 \), the output is \( 23 \).

Would you like any more details or have any questions about the solution?

Here are some related questions to explore further:

1. What would be the output if the input is 5?
2. How would the function change if the rule was \( \text{Output} = \text{Input} \times 3 + 4 \)?
3. If the output is 17, what was the input?
4. What is the general form of the function given in the problem?
5. How does changing the multiplier affect the output?
6. How does changing the constant term affect the output?
7. Can you find the input if the output is given as 13?
8. What happens if the input is a negative number?

### Tip:
When analyzing a function, substitute the given inputs into the function rule and simplify step-by-step to find the outputs.

Learn how to calculate the output of a function machine using the formula Output = Input × 2 + 3 for different input values. This problem covers basic arithmetic operations and function evaluation. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation