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Sketching Polynomial Functions

Sketching Polynomial Functions 1.12 - Solution

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Let's begin by determining the degree of each function. It is determined by the exponent with the highest value. The polynomial function is of degree is of degree and is of degree Now we need to link each graph to its corresponding function by thinking about what the functions' graphs should look in order for them to match.

Graph A

Graph A has the following end behavior. That is consistent with a function with odd degree. We have two polynomial functions with odd degree, and Since the graph is not a linear function, then is not a match. Therefore, we know that the graph must be that of the function

Graph B

Now there are two functions left, and Since the graph B is a parabola, the function has a degree of Therefore, the function is the function for this graph.

Graph C

Since the blue graph is a line it represents a linear function. Thus, we can conclude that it is the graph of