Graphing polynomial functions involves understanding their key features: roots (where the graph crosses the x-axis), y-intercept (where the graph crosses the y-axis), end behavior (what happens to the graph as x approaches positive or negative infinity), and turning points (local maximums and minimums). Worksheets on this topic help you practice identifying these features and sketching the graphs based on the function's equation. These activities also improve understanding of how different terms and coefficients in the polynomial equation affect the shape and position of the graph.
Match each term with its correct definition:
| Term | Definition |
|---|---|
| 1. Root | A. The point where the graph intersects the y-axis. |
| 2. Y-intercept | B. The highest point in a specific section of the graph. |
| 3. End Behavior | C. The value of x where the function equals zero. |
| 4. Local Maximum | D. The direction the graph goes as x approaches infinity. |
| 5. Polynomial | E. An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s). |
Complete the paragraph using the words: degree, leading coefficient, turning points, roots, and y-intercept.
The graph of a polynomial function is determined by several factors. The __________ indicates the highest power of the variable and influences the end behavior. The __________ affects the direction of the graph as x approaches infinity. The __________ are the points where the graph crosses the x-axis, while the __________ is where the graph crosses the y-axis. Finally, __________ are the local maxima and minima of the graph.
Explain how the leading coefficient and the degree of a polynomial function affect its end behavior. Provide an example.
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