91Ó°ÊÓ

The quotient of two polynomial expressions

is a rational expression.

Solve the inequality $3-4x>5$. Graph the solution set.

True or False The graph of a rational function may intersect a vertical asymptote.

Hurricanes In 2005, Hurricane Katrina struck the Gulf Coast of the United States, killing 1289 people and causing an estimated $200 billion in damage. The following data represent the number of major hurricane strikes in the Atlantic Basin (category 3, 4, or 5) each decade from 1921 to 2010.

(a) Draw a scatter diagram of the data. Comment on the type of relation that may exist between the

two variables.

(b) Use a graphing utility to find the cubic function of best fit that models the relation between decade and number of major hurricanes.

(c) Use the model found in part (b) to predict the number of major hurricanes that struck the Atlantic Basin between 1961 and 1970.

(d) With a graphing utility, draw a scatter diagram of the data and then graph the cubic function of best fit on the scatter diagram.

(e) Concern has risen about the increase in the number and intensity of hurricanes, but some scientists believe this is just a natural fluctuation that could last another decade or two. Use your model to predict the number of major hurricanes that will strike the Atlantic Basin between 2011 and 2020. Is your result reasonable?

If a rational function is proper, then______ is a horizontal

asymptote.

Can the graph of a polynomial function have no y-intercept? Can it have no x-intercepts? Explain.

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.

Make up two polynomial functions, not of the same degree, with the following characteristics: crosses the x-axis at $-2$, touches the $x$-axis at $1$, and is above the $x$-axis between $-2$ and $1$. Give your polynomial functions to a fellow classmate and ask for a written critique

True or False. If the degree of the numerator of a rational function equals the degree of the denominator, then the ratio of the leading coefficients give rise to the horizontal asymptote.

The illustration shows the graph of a polynomial function.

(a) Is the degree of the polynomial even or odd?

(b) Is the leading coefficient positive or negative?

(c) Is the function even, odd, or neither?

(d) Why is $x^2$necessarily a factor of the polynomial?

(e) What is the minimum degree of the polynomial?

(f) Formulate five different polynomial functions whose

graphs could look like the one shown. Compare yours to those of other students. What similarities do you see?

What differences?