Lesson 9 - Practice Problems

Transcription

1 Lesson 9 - Practice Problems Section 9.1: Operations on Radical Expressions 1. Perform the indicated operations and simplify your answers a) = b) = c) 6 5 = d) = e) = f) = g) = h) = i) = j) = k) ( 3 + 5) = l) = m) = n) 8 10 ( ) = o) 7 = p) 4 5 = q) 5 = r) = 377

2 . Use the Product Property to simplify each of the following radical expressions. This first one has been done for you. Radical Expression Simplified Form 0 0 = 4 5 = Determine the Radical Conjugate of each of the following radical expressions. Then find the product. The first one has been done for you. Radical Expression Radical Conjugate Product = = = Rationalize the denominator for each of the following. Write your answers in simplest form. 378

3 a) b) c) d) e) f) g) 6 h)

4 Section 9.: Roots, Radicals, and Rational Exponents 5. Complete the table below. Each expression should be written in Radical Notation, written with Rational Exponents and evaluated using a calculator. The first one is done for you. Written in Radical Notation Written Using Rational Exponents Evaluated Using the Calculator (rounded to two decimal places) a) 9 9 9^(1/3).08 b) 0 c) d) 7 e) ( 8) f) 3 g) 11 h) 4 i) ( ) 380

5 6. Evaluate the following using your graphing calculator. If there is no real solution, write N. Round answers to three decimal places if necessary. a) b) 5 c) d) 46 e) 4 f) 4 80 g) 8 h) 8 381

6 Section 9.3: Square Root Functions Key Characteristics 7. Complete the table below. Use DNE if an item does not exist. Function Domain Horizontal Intercept Vertical Intercept a) g x = x b) f( x) = 4x 6 c) f( x) = 4x+ d) s t = 3 t e) h x = 1 6x 38

7 8. Use your graphing calculator to complete the table and sketch the graph of each of the functions below. Use an appropriate viewing window. a) g x = x x g x = x 3 6 b) f( x) = 4x 6 x f( x) = 4x c) f( x) = 4x+ x f( x) = 4x

8 d) s t = 3 t t s t = 3 t 0 3 e) h x = 1 6x x h x = 1 6x

9 Section 9.4: Cube Root Functions Key Characteristics 9. Complete the table below. Function Domain Horizontal Intercept Vertical Intercept 3 a) f ( x) = x b) f ( x) = 9 x 10. Use your graphing calculator to complete the tables and sketch the graphs of the functions below. Use an appropriate viewing window. a) 3 f ( x) = x + 8 x 3 f ( x) = x b) 3 f ( x) = 9 x x 3 f ( x) = 9 x

10 Section 9.5: Solve Radical Equations by Graphing 11. Solve each of the equations by graphing. Round results to three decimal places. Sketch the graph on an appropriate viewing window. Mark and label the solution(s) on your graph. a) x = 16 b) 3 x = 14 c) 4 x 6 = 1 d) x = 0 386

11 e) 5 x 7 = f) 5 3 5x = 11 g) 5 x = x + 17 h) x = x 8 387

12 Section 9.6: Solve Radical Equations Algebraically 1. Solve each equation algebraically. Show all of your work. Round results to three decimal places. Verify that your answers check with the graphical solutions from problem 11. a) x = 16 b) 3 x = 14 c) 4 x 6 = 1 d) x = 0 e) 5 x 7 = f) 5 3 5x =

13 13. Solve each of the equations algebraically. Show all of your work. Round results to three decimal places. Check by graphing. Sketch the graph on an appropriate viewing window. Mark and label the solution(s) on your graph. a) 8 x 7 = x b) x = x c) 4x = x 3 d) x = x

14 Section 9.7: Applications of Radical Equations 14. A person s Body Mass Index, B, is calculated with the formula: B = 703 W H where a) Weight (W) is in pounds and Height (H) is in inches. Rewrite the equation, solving for Height. Show all steps. Height = b) Each of the people listed below have a BMI of 30. Use the formula found in part a) to complete the table. Round to the nearest tenth as needed. Name Weight Height Sara 10 Leonard 78 Marta 155 Dillon 65 Joe 50 Paula

15 15. Voltage through a circuit is determined by the formula V = PR, where P is power, measured in watts, and R is the resistance, measured in ohms. Round answers to two decimal places as needed. a) Determine the amount of resistance that is required for watts of power to produce 4 volts. b) Determine the voltage produced if 100 watts is supplied with a resistance of 40 ohms. c) Determine the amount of power that must be supplied in order to produce 50 volts if the resistance is 30 ohms. 391