A function has the rule “double the input, then add 3.”

Question

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!