.calculator-container {
background-color: #f9f9f9;
border: 1px solid #ddd;
padding: 20px;
border-radius: 8px;
max-width: 600px;
margin: 20px auto;
font-family: Arial, sans-serif;
}
.calculator-container h2 {
text-align: center;
color: #333;
margin-bottom: 20px;
}
.calculator-container p {
margin-bottom: 15px;
line-height: 1.6;
}
.input-group {
margin-bottom: 15px;
padding: 10px;
border: 1px solid #eee;
border-radius: 5px;
background-color: #fff;
}
.input-group h3 {
margin-top: 0;
color: #555;
border-bottom: 1px dashed #eee;
padding-bottom: 10px;
margin-bottom: 10px;
}
.input-group label {
display: block;
margin-bottom: 5px;
font-weight: bold;
color: #444;
}
.input-group input[type="number"],
.input-group input[type="text"],
.input-group select {
width: calc(100% – 12px);
padding: 8px;
margin-bottom: 10px;
border: 1px solid #ccc;
border-radius: 4px;
box-sizing: border-box;
}
.input-group input[type="checkbox"] {
margin-right: 5px;
vertical-align: middle;
}
.input-group div {
margin-bottom: 10px;
}
button {
display: block;
width: 100%;
padding: 10px 15px;
background-color: #007bff;
color: white;
border: none;
border-radius: 4px;
font-size: 16px;
cursor: pointer;
transition: background-color 0.3s ease;
}
button:hover {
background-color: #0056b3;
}
.calculator-result {
margin-top: 20px;
padding: 15px;
border: 1px solid #28a745;
background-color: #e2f9e5;
border-radius: 5px;
font-size: 1.1em;
color: #155724;
word-wrap: break-word;
}
.calculator-result p {
margin: 5px 0;
}
.error-message {
color: #dc3545;
font-weight: bold;
margin-top: 10px;
}
function toggleXStartInputs() {
var xStartType = document.getElementById('xStartType').value;
document.getElementById('xStartValueContainer').style.display = (xStartType === 'specificValue') ? 'block' : 'none';
}
function toggleXEndInputs() {
var xEndType = document.getElementById('xEndType').value;
document.getElementById('xEndValueContainer').style.display = (xEndType === 'specificValue') ? 'block' : 'none';
}
function toggleYStartInputs() {
var yStartType = document.getElementById('yStartType').value;
document.getElementById('yStartValueContainer').style.display = (yStartType === 'specificValue') ? 'block' : 'none';
}
function toggleYEndInputs() {
var yEndType = document.getElementById('yEndType').value;
document.getElementById('yEndValueContainer').style.display = (yEndType === 'specificValue') ? 'block' : 'none';
}
function parseExclusions(exclusionString) {
if (!exclusionString) {
return [];
}
var numbers = exclusionString.split(',').map(function(s) {
return parseFloat(s.trim());
}).filter(function(n) {
return !isNaN(n);
});
// Remove duplicates and sort
return Array.from(new Set(numbers)).sort(function(a, b) { return a – b; });
}
function calculateDomainRange() {
var resultDiv = document.getElementById('result');
resultDiv.innerHTML = "; // Clear previous results
var errorMessage = ";
// — Get X-axis (Domain) Inputs —
var xStartType = document.getElementById('xStartType').value;
var xStartValue = (xStartType === 'specificValue') ? parseFloat(document.getElementById('xStartValue').value) : null;
var xStartInclude = (xStartType === 'specificValue') ? document.getElementById('xStartInclude').checked : false;
var xEndType = document.getElementById('xEndType').value;
var xEndValue = (xEndType === 'specificValue') ? parseFloat(document.getElementById('xEndValue').value) : null;
var xEndInclude = (xEndType === 'specificValue') ? document.getElementById('xEndInclude').checked : false;
var xExclusions = parseExclusions(document.getElementById('xExclusions').value);
// — Get Y-axis (Range) Inputs —
var yStartType = document.getElementById('yStartType').value;
var yStartValue = (yStartType === 'specificValue') ? parseFloat(document.getElementById('yStartValue').value) : null;
var yStartInclude = (yStartType === 'specificValue') ? document.getElementById('yStartInclude').checked : false;
var yEndType = document.getElementById('yEndType').value;
var yEndValue = (yEndType === 'specificValue') ? parseFloat(document.getElementById('yEndValue').value) : null;
var yEndInclude = (yEndType === 'specificValue') ? document.getElementById('yEndInclude').checked : false;
var yExclusions = parseExclusions(document.getElementById('yExclusions').value);
// — Validation —
if (xStartType === 'specificValue' && isNaN(xStartValue)) {
errorMessage += 'Please enter a valid number for X-axis Start Value.';
}
if (xEndType === 'specificValue' && isNaN(xEndValue)) {
errorMessage += 'Please enter a valid number for X-axis End Value.';
}
if (yStartType === 'specificValue' && isNaN(yStartValue)) {
errorMessage += 'Please enter a valid number for Y-axis Start Value.';
}
if (yEndType === 'specificValue' && isNaN(yEndValue)) {
errorMessage += 'Please enter a valid number for Y-axis End Value.';
}
if (xStartType === 'specificValue' && xEndType === 'specificValue' && xStartValue > xEndValue) {
errorMessage += 'X-axis Start Value cannot be greater than X-axis End Value.';
}
if (yStartType === 'specificValue' && yEndType === 'specificValue' && yStartValue > yEndValue) {
errorMessage += 'Y-axis Start Value cannot be greater than Y-axis End Value.';
}
if (errorMessage) {
resultDiv.innerHTML = " + errorMessage + ";
return;
}
// — Calculate Domain —
var domainStartStr, domainStartBracket;
if (xStartType === 'negativeInfinity') {
domainStartStr = '-∞';
domainStartBracket = '(';
} else {
domainStartStr = xStartValue;
domainStartBracket = xStartInclude ? '[' : '(';
}
var domainEndStr, domainEndBracket;
if (xEndType === 'positiveInfinity') {
domainEndStr = '∞';
domainEndBracket = ')';
} else {
domainEndStr = xEndValue;
domainEndBracket = xEndInclude ? ']' : ')';
}
var domainResult = 'Domain: ' + domainStartBracket + domainStartStr + ', ' + domainEndStr + domainEndBracket;
if (xExclusions.length > 0) {
domainResult += ' excluding {' + xExclusions.join(', ') + '}';
}
// — Calculate Range —
var rangeStartStr, rangeStartBracket;
if (yStartType === 'negativeInfinity') {
rangeStartStr = '-∞';
rangeStartBracket = '(';
} else {
rangeStartStr = yStartValue;
rangeStartBracket = yStartInclude ? '[' : '(';
}
var rangeEndStr, rangeEndBracket;
if (yEndType === 'positiveInfinity') {
rangeEndStr = '∞';
rangeEndBracket = ')';
} else {
rangeEndStr = yEndValue;
rangeEndBracket = yEndInclude ? ']' : ')';
}
var rangeResult = 'Range: ' + rangeStartBracket + rangeStartStr + ', ' + rangeEndStr + rangeEndBracket;
if (yExclusions.length > 0) {
rangeResult += ' excluding {' + yExclusions.join(', ') + '}';
}
resultDiv.innerHTML = " + domainResult + " + rangeResult + ";
}
// Initial calls to set correct display states
toggleXStartInputs();
toggleXEndInputs();
toggleYStartInputs();
toggleYEndInputs();
Understanding Domain and Range from a Graph
When analyzing a function, two fundamental concepts are its domain and range. These describe the set of all possible input values (x-values) and output values (y-values) for which the function is defined. Understanding how to determine these from a graph is a crucial skill in mathematics.
What is Domain?
The domain of a function refers to all the possible input values (x-values) for which the function is defined. On a graph, the domain represents the extent of the graph along the horizontal (x) axis. To find the domain from a graph, you essentially "squish" the entire graph onto the x-axis and observe which x-values are covered.
- If the graph extends indefinitely to the left, the domain includes negative infinity (-∞).
- If the graph extends indefinitely to the right, the domain includes positive infinity (∞).
- If there are specific points or intervals where the graph starts or ends, those values define the boundaries of the domain.
- Open circles or dashed lines at a point indicate that the value is excluded (use parentheses).
- Closed circles or solid lines indicate that the value is included (use square brackets).
- Vertical asymptotes or holes in the graph indicate specific x-values that are excluded from the domain.
What is Range?
The range of a function refers to all the possible output values (y-values) that the function can produce. On a graph, the range represents the extent of the graph along the vertical (y) axis. To find the range from a graph, you "squish" the entire graph onto the y-axis and observe which y-values are covered.
- If the graph extends indefinitely downwards, the range includes negative infinity (-∞).
- If the graph extends indefinitely upwards, the range includes positive infinity (∞).
- Similar to the domain, specific points or intervals where the graph starts or ends vertically define the boundaries of the range.
- Horizontal asymptotes or holes in the graph indicate specific y-values that are excluded from the range.
How to Use the Calculator
This calculator helps you formalize the domain and range you observe from a graph:
- Define X-axis Extent (Domain):
- Choose whether the graph starts at negative infinity or a specific value on the x-axis. If a specific value, indicate if it's included (closed bracket) or excluded (open parenthesis).
- Do the same for the end of the x-axis extent (positive infinity or a specific value).
- If there are any vertical asymptotes or holes in the graph, list their x-values in the "X-axis Exclusions" field, separated by commas.
- Define Y-axis Extent (Range):
- Similarly, choose whether the graph starts at negative infinity or a specific value on the y-axis. Indicate inclusion/exclusion.
- Do the same for the end of the y-axis extent.
- If there are any horizontal asymptotes or holes in the graph, list their y-values in the "Y-axis Exclusions" field, separated by commas.
- Click "Calculate Domain & Range" to see the results in interval notation.
Examples:
Example 1: A Parabola (e.g., y = x²)
Imagine a standard parabola opening upwards, with its vertex at (0,0).
- X-axis Start: Negative Infinity
- X-axis End: Positive Infinity
- X-axis Exclusions: (leave blank)
- Y-axis Start: Specific Value (0), Include Value (checked)
- Y-axis End: Positive Infinity
- Y-axis Exclusions: (leave blank)
Result:
Domain: (-∞, ∞)
Range: [0, ∞)
Example 2: A Rational Function (e.g., y = 1/x)
Consider the graph of y = 1/x, which has asymptotes at x=0 and y=0.
- X-axis Start: Negative Infinity
- X-axis End: Positive Infinity
- X-axis Exclusions: 0
- Y-axis Start: Negative Infinity
- Y-axis End: Positive Infinity
- Y-axis Exclusions: 0
Result:
Domain: (-∞, ∞) excluding {0}
Range: (-∞, ∞) excluding {0}
Example 3: A Line Segment
Consider a line segment from point (1, 2) to (5, 8), including both endpoints.
- X-axis Start: Specific Value (1), Include Value (checked)
- X-axis End: Specific Value (5), Include Value (checked)
- X-axis Exclusions: (leave blank)
- Y-axis Start: Specific Value (2), Include Value (checked)
- Y-axis End: Specific Value (8), Include Value (checked)
- Y-axis Exclusions: (leave blank)
Result:
Domain: [1, 5]
Range: [2, 8]