1 / 10

Chapter 8

Chapter 8. Rational Functions. Chapter Summary. 8.1: Model Inverse and Joint Variation 8.2: Graph Simple Rational Functions Quiz 8.3: Graph General Rational Functions 8.4: Multiply and Divide Rational Expressions Quiz 8.5: Add and Subtract Rational Functions 8.6: Solve Rational Equations

zita
Download Presentation

Chapter 8

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Chapter 8 Rational Functions

  2. Chapter Summary • 8.1: Model Inverse and Joint Variation • 8.2: Graph Simple Rational Functions • Quiz • 8.3: Graph General Rational Functions • 8.4: Multiply and Divide Rational Expressions • Quiz • 8.5: Add and Subtract Rational Functions • 8.6: Solve Rational Equations • Quiz • Chapter 8 Test

  3. Section 8.1 Model Inverse and Joint Variation

  4. Direct and Inverse Variation • Two variables x and y vary directly if there is a nonzero number a such that the following is true: • Two variables x and y show inverse variation if they are related as follows: Constant of Variation

  5. y = y c. = x 4 7 x Classify Tell whether xand yshow direct variation, inverse variation, or neither. Type of Variation Given Equation Rewritten Equation a.xy = 7 Inverse b.y = x + 3 Neither Direct y = 4x 1. 3x = y 2.xy = 0.75 3.y = x –5 Direct Inverse Neither

  6. y= 7= 28 The inverse variation equation is y = x a a 12 x 4 = 6. Whenx = 2,y = 2 12 –14. Whenx = –2, y = y = x Write Inverse Variation Equation The variables xand yvary inversely, and y = 7 when x=4. Write an equation that relates xand y. Then find ywhen x = –2 . Write general equation for inverse variation. Substitute 7 for yand 4 for x. 28 = a Solve for a. ANSWER 4.x = 4,y = 3 ANSWER

  7. Joint Variation • Joint variation occurs when a quantity varies directly with the product of two or more quantities. In the equations below, a is a nonzero constant. z = axy z varies jointly with x and y. p = aqrs p varies jointly with q, r and s.

  8. STEP 1 Write a general joint variation equation. STEP2 Use the given values of z, x, and y to find the constant of variation a. Write a Joint Variation Equation The variable zvaries jointly with xand y. Also, z= –75 when x = 3 and y = –5. Write an equation that relates x, y, and z. Then find zwhen x = 2 and y = 6. SOLUTION z= axy –75 = a(3)(–5) Substitute 75 for z, 3 for x, and 25 for y. –75 = –15a Simplify. 5 = a Solve for a.

  9. ANSWER ; – 35 ANSWER z = – 2xy ; 20 7 z = xy 2 Write a Joint Variation Equation STEP 3 Rewrite the joint variation equation with the value of afrom Step 2. z = 5xy STEP 4 Calculate zwhen x = 2 and y = 6 using substitution. z = 5xy= 5(2)(6) = 60 The variable zvaries jointly with xand y. Use the given values to write an equation relating x, y, and z. Then find zwhen x = –2 and y = 5. 9.x = 1,y = 2,z = 7 10.x = 4,y = –3,z =24

  10. y = y = z = atr x = s ay a a x x2 x Compare Different Types of Variation Write an equation for the given relationship. Relationship Equation a.yvaries inversely with x. b.zvaries jointly with x, y, and r. z = axyr c.y varies inversely with the square of x. d.zvaries directly with yand inversely with x. e.xvaries jointly with tand rand inversely with s.

More Related