What is the graph of the rational function?
y=(x−4)(x−1)(x+5)(x−5)
(1 point)
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graph
Image with alt text: graph
graph
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Without a specific graph provided, it is difficult to accurately describe the graph of the rational function y=(x−4)(x−1)(x+5)(x−5). However, based on the factors in the function, we can infer some key points about the graph.
- The function has roots at x=4, x=1, x=-5, and x=5. This means the graph will have x-intercepts at these points.
- The degree of the function is 4, so we can expect the graph to have a maximum of 3 turning points.
- The end behavior of the function will be determined by the leading term, which is x^4. This means the graph will approach positive infinity as x approaches infinity and negative infinity as x approaches negative infinity.
In general, the graph of the given rational function will be a smooth curve that passes through the x-intercepts at x=4, x=1, x=-5, and x=5. The exact shape of the graph will depend on the behavior of the function between these points.