Exam 3 Review

Polynomial Functions

100

Is it possible to have a polynomial of degree 7 without any x-intercepts? Why or why not?

It is not possible to have one because the polynomial has an odd degree, therefore the end behavior is opposite so at some point the function MUST cross the x-axis.

200

g(x)= -x^5 +5x^3 -4x Answer the following: Degree, LC, End Behavior, Max # of X-intercepts, Max # of Turning Points

What is Degree: 5 LC: -1 EB:Up, Down Max X's: 5 Max TP's: 4

300

Is it possible to have a polynomial function with degree 10 that falls to the left and falls to the right? Why or why not?

What is yes it is possible because with an even degree polynomial, the end behaviors MUST be the same.

400

f(x)=x(x^2 -4) Find the following: Degree, LC, End Behavior, Max # of X-intercepts, and the Max # of Turning Points

What are Degree: 3 LC: 1 EB: Down, Up Max X's: 3 Max TP's: 2

500

Is it possible to have a polynomial function of degree 9 with 3 valleys and 3 hills? Why or why not?

What is yes, it is possible because there can be up to 8 turning points an 3 valleys and 3 hills creates opposite end behavior.

Polynomial Regression

100

The immigration population (in millions) living in the US at the beginning of each decade from 1900 to 2000 is given by the following: (Year: 1900, 1910, 1920, 1930, 1940, 1950, 1960, 1970, 1980, 1990, 2000 Population: 10.3, 13.5, 13.9, 14.2, 11.6, 10.3, 9.7, 9.6, 14.1, 19.8, 30) Which type of regression is appropriate? Find the Model.

What is Cubic; y= (1.323E^-4)x^3 -0.016x^2 +0.465x +10.287

200

The following gives the results from a University test farm, where researchers compared the density of corn planting to crop yield. (Density (thousands of plants per acre):15, 20, 25, 30, 35, 40, 45, 50 Crop Yield (bushels per acre): 43, 98, 118, 140, 142, 122, 93, 67) Determine the appropriate type of regression and find the model.

What is Quadratic; y= -0.278x^2 +18.465x -166.732

300

The following represents the average dollar amount that a family gives to charity based on the annual income in thousands of dollars. (Annual Income (in thousands): 5, 25, 45, 65, 86, 100 Charitable Contributions (in dollars): 256, 727, 814, 1191, 2528, 4565) Which type of regression is appropriate? Find the model.

What is both? Cubic and quartic fit this stat plot well, the models would be as follows: Cubic: y= .0148x^3 -1.6601x^2 +63.3618x -29.5851 Quartic: y= (5.021E^-5)x^4 +0.004x^3 -0.947x^2 +46.972x +46.547

400

The following represents clothing sales and their tendency to very by season. (Month: January (1), February, March, April, May, June, July, August, September, October, November, December (12) Sales (in thousands): 8, 18, 22, 31, 29, 21, 22, 26, 38, 40, 27, 15) Determine the appropriate type of regression and find the model.

What is quartic regression fits this function best? y= -0.056x^4 +1.415x^3 -12.199x^2 +42.577x -25.715

500

A psychologist asked several subjects to list as many types of vegetables as they could in 30 seconds. The average results are as follows: (Seconds: 1, 2, 5, 10, 15, 20, 25, 30 # of Vegetables: 2, 6, 10, 12, 14, 15, 18, 21) Determine the most appropriate type of regression and find the model.

What is quadratic because the r^2 value is closer to 1 than it is with the other types of regression? y= -1.57x^4 +.01x^3 -.30x^2 +3.24x -0.26

Polynomial Inequalities

100

Solve the inequality and put it in interval notation. (x-4)(x+3)<0

What is (-3, 4)?

200

Solve the equation and put it in interval notation. (x+5)(x-2)(x-1)(x+1)<0

What is (-5, -1)U(1,2)?

300

Solve the inequality and put it in interval notation. x^2 +5x +4 < (or equal to) 0

What is [-4, -1]?

400

Solve the inequality and put it in interval notation. (x+8)(x+2)(x-3)>(or equal to) 0

What is [-8,-2]U[3, infinity)?

500

Solve the inequality and put it in interval notation. x^2 -14x +49 >(or equal to) 0

What is (negative infinity, infinity)?

Rational Functions

100

Find the Domain, VA, HA, Holes, Xint, and the Yint of the following function. f(x)= (2.5x+1800)/x

What is domain: all reals except 0, VA: at x=0, HA: at y=2.5, Holes: none, xint: at x=-720, yint: none?

200

f(x)=(80,000p)/(100-p) Find the domain, VA, HA, Holes, P-ints, and the Y-int.

What is domain: all reals except 100, VA: at p=100, HA: at y=-80,000, Holes: none, P-ints: at p=0, Y-int: y=0

300

f(x)= 1/x Find the domain, VA, HA, Holes, Xints, and Yint.

What is domain: all reals except 0, VA: at x=0, HA: at y=0, Holes: none, Xint: none, Yint: none?

400

Write a function with the following characteristics. A hole at x=3 and a HA at y=6 There are many possible answers.

What is 6x/(x-3)?

500

Find a function with the following characteristics. An xintercept at x= -7, a VA at x=9, a HA at y=3, and a hole at x=-2

What is 3(x+7)(x+2)/(x-9)(x+2)?

Rational Inequalities

100

(x+3)(x+5)/(x+2)>(or equal to) 0 Solve the inequality in interval notation.

What is [-5, -3]U(-2, infinity)?

200

Solve the inequality in interval notation. (x+68)/(x+8)>(or equal to) 5

What is (-8, 7]?

300

Solve the inequality in interval notation. (x+6)/(x^2 -5x-24) > 0

What is (-6, -3)U(8, infinity)?

400

Solve the inequality in interval notation. -7/(x+5) <(or equal to) -8/(x+6)

What is (negative infinity, -6)U(-5, 2]?

500

Write a rational inequality with the solution: (-2, -1)U(1, infinity).

What is (x+1)(x+2)/(x-1) > 0?