91Ó°ÊÓ

The common cold is caused by a rhinovirus. After \(x\) days of invasion by the viral particles, the number of particles in our bodies, \(f(x),\) in billions, can be modeled by the polynomial function $$ f(x)=-0.75 x^{4}+3 x^{3}+5 $$ Use the Leading Coefficient Test to determine the graphs end behavior to the right. What does this mean about the number of viral particles in our bodies over time?

Explain why the equation \(x^{4}+6 x^{2}+2=0\) has no rational roots.

Explain the relationship between the multiplicity of a zero and whether or not the graph crosses or touches the \(x\) -axis at that zero.

Determine a number of polynomial functions of odd degree and graph each function. Is it possible for the graph to have no real zeros? Explain. Try doing the same thing for polynomial functions of even degree. Now is it possible to have no real zeros?

Explain why nonreal complex zeros are gained or lost in pairs in terms of graphs of polynomial functions.

Describe a strategy for graphing a polynomial function. In your description, mention intercepts, the polynomials degree, and turning points.

Find the axis of symmetry for each parabola whose equation is given. Use the axis of symmetry to find a second point on the parabola whose y-coordinate is the same as the given point. \(f(x)=3(x+2)^{2}-5 ; \quad(-1,-2)\)

Give an example of a function that is not subject to the Intermediate Value Theorem.

Among all deaths from a particular disease, the percentage that are smoking related ( \(21-39\) cigarettes per day) is a function of the disease's incidence ratio. The incidence ratio describes the number of times more likely smokers are than nonsmokers to die from the disease. The following table shows the incidence ratios for heart disease and lung cancer for two age groups. Incidence Ratios $$\begin{array}{|l|cc|} \hline & \text { Heart Disease } & \text { Lung Cancer } \\ \hline \text { Ages } 55-64 & 1.9 & 10 \\ \text { Ages } 65-74 & 1.7 & 9 \\ \hline \end{array}$$ For example, the incidence ratio of 9 in the table means that smokers between the ages of 65 and 74 are 9 times more likely than nonsmokers in the same group to die from lung cancer. The rational function $$P(x)=\frac{100(x-1)}{x}$$ models the percentage of smoking-related deaths among all deaths from a disease, \(P(x),\) in terms of the disease's incidence ratio, \(x\). The graph of the rational function is shown. Use this function to solve Exercises . (graph can't copy) Find \(P(9) .\) Round to the nearest percent. Describe what this means in terms of the incidence ratio, 9 given in the table. Identify your solution as a point on the graph.

If you are given the equation of a rational function, explain how to find the horizontal asymptote, if any, of the functions graph.