Polynomial and Rational Functions Active Learning Lecture Slides For use with Classroom Response Systems © 2009 Pearson Education, Inc. All rights reserved. Chapter 5 Polynomial and Rational Functions

State whether is a polynomial Function or not. If it is, give its degree. If it is not, tell why. a. No; x is raised to non-integer 4/3 power b. Yes; degree 3 c. Yes; degree 4/3 d. Yes; degree 4

State whether is a polynomial Function or not. If it is, give its degree. If it is not, tell why. a. No; x is raised to non-integer 4/3 power b. Yes; degree 3 c. Yes; degree 4/3 d. Yes; degree 4

Use transformations of y = x5 to graph b. c. d.

Use transformations of y = x5 to graph b. c. d.

Form a polynomial of degree 3 with zeros: –3, –1, and 2. b. c. d.

Form a polynomial of degree 3 with zeros: –3, –1, and 2. b. c. d.

For the polynomial List each zero, its multiplicity and whether the graph crosses or touches the x-axis. a. 0, mult. 2, crosses axis; 5, mult. 1, touches axis; , mult. 1, touches axis; , mult. 1, touches axis; b. 0, mult. 2, touches axis; 5, mult. 1, crosses axis; , mult. 1, crosses axis; , mult. 1, crosses axis; c. 0, mult. 2, touches axis; 5, mult. 1, crosses axis; d. 0, mult. 2, crosses axis; 5, mult. 1, touches axis;

For the polynomial List each zero, its multiplicity and whether the graph crosses or touches the x-axis. a. 0, mult. 2, crosses axis; 5, mult. 1, touches axis; , mult. 1, touches axis; , mult. 1, touches axis; b. 0, mult. 2, touches axis; 5, mult. 1, crosses axis; , mult. 1, crosses axis; , mult. 1, crosses axis; c. 0, mult. 2, touches axis; 5, mult. 1, crosses axis; d. 0, mult. 2, crosses axis; 5, mult. 1, touches axis;

Find the x- and y-intercepts of a. x-intercepts: –6, 0, 1; y-intercept: –6 b. x-intercepts: –1, 0, 1, 6; y-intercept: 0 c. x-intercepts: –6, –1, 0, 1; y-intercept: 0 d. x-intercepts: –6, –1, 0, 1; y-intercept: –6

Find the x- and y-intercepts of a. x-intercepts: –6, 0, 1; y-intercept: –6 b. x-intercepts: –1, 0, 1, 6; y-intercept: 0 c. x-intercepts: –6, –1, 0, 1; y-intercept: 0 d. x-intercepts: –6, –1, 0, 1; y-intercept: –6

The price of electric guitars has varied considerably in recent years The price of electric guitars has varied considerably in recent years. The data in the table relates the price in dollars, to time in years, where 1 represents 1998. Use a cubic function fitted to the data to predict the price of an electric guitar in 2007. Year, x $, P 1998, 1 $618.20 1999, 2 $783.20 2000, 3 $674.30 2001, 4 $721.60 2002, 5 $825.00 2003, 6 $891.00 2004, 7 $852.50 2005, 8 $819.50 2006, 9 a. $443.52 b. $827.42 c. $670.48 d. $893.53

The price of electric guitars has varied considerably in recent years The price of electric guitars has varied considerably in recent years. The data in the table relates the price in dollars, to time in years, where 1 represents 1998. Use a cubic function fitted to the data to predict the price of an electric guitar in 2007. Year, x $, P 1998, 1 $618.20 1999, 2 $783.20 2000, 3 $674.30 2001, 4 $721.60 2002, 5 $825.00 2003, 6 $891.00 2004, 7 $852.50 2005, 8 $819.50 2006, 9 a. $443.52 b. $827.42 c. $670.48 d. $893.53

Find the domain and range of b. c. d. All real numbers

Find the domain and range of b. c. d. All real numbers

Use the graph to determine the domain and range of the function. a. D: all real numbers R: all real numbers b. D: R: c. D: R: d. D: R:

Use the graph to determine the domain and range of the function. a. D: all real numbers R: all real numbers b. D: R: c. D: R: d. D: R:

Use the graph to find the vertical asymptote, if any, of the function. a. x = –3, x = 3 b. x = –3, x = 3, x = 0 c. x = –3, x = 3, y = 0 d. none

Use the graph to find the vertical asymptote, if any, of the function. a. x = –3, x = 3 b. x = –3, x = 3, x = 0 c. x = –3, x = 3, y = 0 d. none

Give the equation of the oblique asymptote, if any, of the function a. b. c. d.

Give the equation of the oblique asymptote, if any, of the function a. b. c. d.

Graph a. b. c. d.

Graph a. b. c. d.

Graph a. b. c. d.

Graph a. b. c. d.

The concentration of a drug in the bloodstream, measured in milligrams per liter, can be modeled by the function where t is the number of minutes after the injection of the drug. Find the value of t (rounded to two decimal places) for which the drug will be at its highest concentration. a. t = 0.55 b. t = 3.65 c. t = 0 d. t = 4

The concentration of a drug in the bloodstream, measured in milligrams per liter, can be modeled by the function where t is the number of minutes after the injection of the drug. Find the value of t (rounded to two decimal places) for which the drug will be at its highest concentration. a. t = 0.55 b. t = 3.65 c. t = 0 d. t = 4

Use the graph of the function f to solve the inequality f(x) > 0. b. c. d.

Use the graph of the function f to solve the inequality f(x) > 0. b. c. d.

Solve the inequality algebraically. d.

Solve the inequality algebraically. d.

Solve the inequality algebraically. d.

Solve the inequality algebraically. d.

Use the Remainder Theorem to find the remainder when is divided by x + 1. c. 21 d. –21

Use the Remainder Theorem to find the remainder when is divided by x + 1. c. 21 d. –21

Use the Factor Theorem to determine whether x + 9 is a factor of If it is, write f in factored form. a. Yes; b. Yes; c. Yes; d. No

Use the Factor Theorem to determine whether x + 9 is a factor of If it is, write f in factored form. a. Yes; b. Yes; c. Yes; d. No

List the potential rational zeros of b. c. d.

List the potential rational zeros of b. c. d.

Use the Rational Zeros theorem to find all real zeros of Use the zeros to factor f over the real numbers. a. b. c. d.

Use the Rational Zeros theorem to find all real zeros of Use the zeros to factor f over the real numbers. a. b. c. d.

Find the real solutions of b. c. d.

Find the real solutions of b. c. d.

Find a bound on the real zeros of a. –10 and 10 b. – 6 and 6 c. –15 and 15 d.

Find a bound on the real zeros of a. –10 and 10 b. – 6 and 6 c. –15 and 15 d.

Use the Intermediate Value Theorem to determine whether has a zero in the interval [–1, 0]. b. c. d.

Use the Intermediate Value Theorem to determine whether has a zero in the interval [–1, 0]. b. c. d.

Form a polynomial f (x) with real coefficients having degree 3 and zeros 1 + i and –6. b. c. d.

Form a polynomial f (x) with real coefficients having degree 3 and zeros 1 + i and –6. b. c. d.

Find all zeros of and write f as a product of linear factors. b. c. d.

Find all zeros of and write f as a product of linear factors. b. c. d.