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

Answer 1

To represent the rule "double the input, then add 3" using the variable \( x \) for the input, we can follow the step-by-step breakdown:

1. Double the input \( x \): This is represented as \( 2x \).
2. Then add 3 to the result of doubling the input: This can be expressed as \( 2x + 3 \).

So, the expression that represents the rule "double the input, then add 3" is:

\[
y = 2x + 3
\]

Here’s how you would complete the diagram:

- Input: \( x \)
- Output: \( y \)
- The relationship (arrow) between them: \( y = 2x + 3 \)

This means for any input value \( x \), you would first double it, and then add 3 to get the output \( y \).