Write a few paragraphs that provide a general strategy for graphing a polynomial function. Be sure to mention the following: degree, intercepts, end behavior, and turning points.
For graphing the polynomial, find the intercept nad zeroes of the polynomial.
First of all, we should determine the end behavior of the function that is how the function will behave for large values of . This is helpful in guessing the shape of the graph. Then, we should know the and intercept of the graph. This can be found putting and .
We need to know the zeroes of the polynomial. This can be found by putting the polynomial function equal to zero. This will tell us the point at which the graph crosses or touches the axis
We should know the domain and range of the function. For a polynomial function, the domain is generally all real numbers. The range however can vary depending on the polynomial function.
Then, we should know the turning points that are the maxima and minima of the function. This can be found using the first derivative test. This test involves taking the equating the first derivative of the polynomial function equal to zero. The values of obtained will be the turning points of the polynomial function.
The concentration C of a certain drug in a patient's bloodstream t hours after injection is given by
Part (a): Find the horizontal asymptote of . What happens to the concentration of the drug as t increases?
Part (b): Using your graphing utility, graph .
Part (c): Determine the time at which the concentration is highest.
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