Question

A function has the rule “double the input, then add 3.”
Using x to represent the input, complete the diagram with an expression for this rule. What expression represents “double the input, then add 3?”
x
Input Output Arrow
Input Output Arrow
y
Good work!
Next, determine the independent and dependent variables for this function. You can use your diagram to help you.
x
Input Output Arrow
2x + 3
Input Output Arrow
y
The independent variable is
x .

The dependent variable is
y .
Great job!
Now, write an equation that represents this function. You can use the diagram to help you.
x
Input Output Arrow
2x + 3
Input Output Arrow
y

Answer 1

Based on the rule "double the input, then add 3,” we can define the function clearly in a diagram as follows:

1. **Expression for the Rule:**
- Input: \(x\)
- Output: \(2x + 3\)
- This can be shown in a diagram as:
```
x → 2x + 3 → y
```

2. **Identifying Independent and Dependent Variables:**
- The independent variable is \(x\) (the input).
- The dependent variable is \(y\) (the output).

3. **Equation that Represents this Function:**
- The equation that represents this function can be written as:
\[
y = 2x + 3
\]

Putting it all together, we have:

- **Input:** \(x\)
- **Output:** \(2x + 3\)
- **Independent Variable:** \(x\)
- **Dependent Variable:** \(y\)
- **Equation:** \(y = 2x + 3\)

This summarizes the entire function and its components accurately!