Source: https://guthlabs.ai/docs/instruments/function-transformation-visualizer/implementation/

instrument implementation / implementation-contract

# Function Transformation Visualizer implementation

A source-bound implementation contract for Function Transformation Visualizer; deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t8-031

**Effect**: Computation or source lookup only

## Input and validation requirements

Setting b=0 with the parent function f(u)=1/u makes the transformed argument identically zero and causes division by zero for every x. The visualizer should reject the input or display an undefined-function state rather than attempting a finite plot.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "parent_function": "f(x)=x^2",
    "a": "2",
    "b": "3",
    "h": "1",
    "k": "-4",
    "sample_x": [
      "0.0000000",
      "1.0000000",
      "1.3333333333333333"
    ]
  },
  "expected_outputs": {
    "exact_transformed_function": "g(x)=2[3(x-1)]^2-4=18(x-1)^2-4",
    "sample_values": [
      {
        "x": 0,
        "g_x": 14
      },
      {
        "x": 1,
        "g_x": -4
      },
      {
        "x": 1.3333333333333333,
        "g_x": -2
      }
    ],
    "spot_checks": [
      {
        "at": "0",
        "input_side": 14,
        "answer_side": 14
      },
      {
        "at": "1",
        "input_side": -4,
        "answer_side": -4
      },
      {
        "at": "4/3",
        "input_side": -2,
        "answer_side": -2
      }
    ]
  },
  "reference_data": {
    "parent_vertex": [
      0,
      0
    ],
    "transformed_vertex": [
      1,
      -4
    ],
    "point_mapping": "(u,f(u)) maps to (h+u/b,a·f(u)+k)"
  },
  "working": "At x=0: b(x-h)=3(0-1)=-3; f(-3)=(-3)^2=9; g(0)=2·9-4=18-4=14. At x=1: b(x-h)=3(1-1)=0; f(0)=0; g(1)=2·0-4=-4. At x=4/3: b(x-h)=3(4/3-1)=3·(1/3)=1; f(1)=1; g(4/3)=2·1-4=-2. Algebraically, 2[3(x-1)]^2-4=2·9(x-1)^2-4=18(x-1)^2-4."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/function-transformation-visualizer/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/function-transformation-visualizer/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/function-transformation-visualizer/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche8/tranche8-results.json`