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Learn about functions and graphs, verify domains and ranges, and use the vertical line test to determine if a curve represents a function. Discover the natural domain, arrow diagrams, and examples for a comprehensive understanding.
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Section 1.3 Functions and Their Graphs الدوال ورسمها
X Y X Y 1 2 3 a b 1 2 3 a b c X Y 1 2 a b c X Y X Y 1 2 a b c 1 2 3 a b التمثيل السهمي Arrow diagram
Example 1: Verify the domains and ranges of the following functions المجال الطبيعي Natural domain
The Vertical Line Test Notice that not every curve is the graph of a function, since for a function, only one y-value corresponds to a given value of x. You can graphically determine whether a curve is the graph of a function by using the vertical line test: if any vertical line intersects the graph in more than one point, the curve is not the graph of a function.