The image depicts a graph of a mathematical function on a Cartesian plane with axes labeled as \(x\) and \(y\). Here is a detailed explanation of the key features of the graph: 1. **Axes**: The horizontal axis represents the \(x\)-axis, and the vertical axis represents the \(y\)-axis. 2. **Graph Description**: - The graph features a curve that crosses the \(x\)-axis at two points: approximately \(-1\) and \(1\). - The graph rises to a peak (local maximum) at the point \((0, 2)\). - After this peak, the graph descends and has a local minimum at \((1, 0)\). - The curve then continues downward and crosses below the \(x\)-axis. 3. **Intercepts**: - **\(x\)-Intercepts**: The points where the graph crosses the \(x\)-axis include \((-1, 0)\) and \( (1, 0)\). - **\(y\)-Intercept**: The graph does not explicitly highlight a \(y\)-intercept, but it suggests a value of \(2\) for the vertex at \( (0, 2)\). 4. **Behavior**: - The graph suggests a polynomial function with a wavy pattern, showing one peak and one trough. - The end behavior of the graph indicates that as \(x\) approaches positive infinity, \(y\) decreases, and as \(x\) approaches negative infinity, \(y\) increases. This is typical of a cubic polynomial with a negative leading coefficient. This graph can be used to study the properties of polynomial functions, including understanding roots, turning points, and behavior at infinity.

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.