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Chapter 3: Problem 51
State the Remainder Theorem.
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In Exercises \(1-10\), determine which functions are polynomial functions. For those that are, identify the degree. $$f(x)=\frac{x^{2}+7}{3}$$
The heat generated by a stove element varies directly as the square of the voltage and inversely as the resistance. If the voltage remains constant, what needs to be done to triple the amount of heat generated?
The rational function $$f(x)=\frac{27,725(x-14)}{x^{2}+9}-5 x$$ models the number of arrests, \(f(x)\), per \(100,000\) drivers, for driving under the influence of alcohol, as a function of a driver's age, \(x\) a. Graph the function in a \([0,70,5]\) by \([0,400,20]\) viewing rectangle. b. Describe the trend shown by the graph. c. Use the ZOOM and TRACE features or the maximum function feature of your graphing utility to find the age that corresponds to the greatest number of arrests. How many arrests, per \(100,000\) drivers, are there for this age group?
In Exercises \(1-10\), determine which functions are polynomial functions. For those that are, identify the degree. $$g(x)=6 x^{7}+\pi x^{5}+\frac{2}{3} x$$
In Exercises \(35-50\) a. Use the Leading Coefficient Test to determine the graphs end behavior. b. Find \(x\) -intercepts by setting \(f(x)=0\) and solving the resulting polynomial equation. State whether the graph crosses the \(x\)-axis, or touches the \(x\)-axis and turns around, at each intercept. c. Find the \(y\) -intercept by setting \(x\) equal to 0 and computing \(f(0)\) d. Determine whether the graph has \(y\) -axis symmetry, origin symmetry, or neither. e. If necessary, find a few additional points and graph the function. Use the fact that the maximum number of turning points of the graph is \(n-1\) to check whether it is drawn correctly. $$f(x)=-2 x^{4}+4 x^{3}$$
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