Here are the essential concepts you must grasp in order to answer the question correctly.
Function Definition
A function is a relation where each input (x-value) corresponds to exactly one output (y-value). This means that for any given x, there should be only one y. To determine if y is a function of x, one can use the vertical line test: if a vertical line intersects the graph at more than one point, then y is not a function of x.
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Domain and Range
The domain of a function is the set of all possible input values (x-values) that can be used without causing any mathematical issues, such as division by zero or taking the square root of a negative number. The range is the set of all possible output values (y-values) that result from the function. Understanding the domain and range is crucial for analyzing the behavior of the function represented by the graph.
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Graph Interpretation
Interpreting a graph involves analyzing its shape, direction, and points of intersection with the axes. This includes identifying key features such as intercepts, asymptotes, and continuity. By examining these elements, one can gain insights into the nature of the relationship between x and y, which is essential for determining if y is a function of x and for identifying the domain and range.
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