1.6 objective: Quiz on Friday

Transcription

1 1.6 objective: Next year: Students will be able to find inverse functions. Students will be able to tell if two functions are inverses algebraically, graphically, and numerically (by table). Quiz on Friday The test is on block day Thursday Sept. 15th. Any homework that is turned in before Thursday can still get full credit. After the test the homework receives partial credit. Any student who does not have at least 75% homework (that does not look like it has been copied from BoB or calcchat). Can not retake the test. If a student has not gone to tutor room and or access for help before the test they can not retake the test. In other words if I am not convinced you genuinely tried to prepare and study the first time, you will not get a second time WARM UP Describethesetoftransformationsneededtochangetheparentfunctiontothe givenfunction.howisthegivenfunctiondifferentfromtheparentfunction?be veryspeciicbyincludingthedirectionandhowmanyunits.leavethespaceblank ifitdoesnotapply. Horizontal Shift Vertical Shift Reflection Non Rigid (Vertical Stretch/Shrink) 1

2 1.6 Inverse Functions Let f and g be two functions. If f(g(x))= x for every x in the domain of g and g(f(x))= x for every x in the domain of f, then g is the inverse function of the function f. The function g is denoted by English please: To find out if 2 functions are inverses of each other, put g into f, simplify to see if you get x. Then put f into g and simplify to see if you get x. If you get x BOTH times, then the functions are inverses. N numerical For a function f that is defined by a set of ordered pairs, to form the inverse function of f, interchange the x and y coordinates (the domain and range). Example f(x)= {(1,5), (2,6), (3,7), (4,8)} f 1 (x)= f(x) f 1 (x)

3 2. Verify that the functions are Inverse functions graphically and numerically. f(x) = 2x 3 1 g(x) = x If the first graph has a point at ( 3, 55) the other graph needs to have a point at ( 55, 3).... In this chart we can see the point at (0, 1) and ( 1, 0) Graph and it's inverse. With NO calculator. discussion: 3

4 Existence of Inverse Functions A function f has an inverse f 1 iff (if and only if) f is oneto one. One to one (1:1) means that no two elements in the domain of the function correspond to the same element in the range of the function. In this course we will only verify graphically. If it passes the horizontal line test then it is one to one. Is the graph a function? Is the graph one to one? Does the graph have an inverse FUNCTION? If yes, then sketch it. 4

5 Sketch the graph of with out the calculator. Is the graph a function? Is the graph one to one? Does the graph have an inverse FUNCTION? If yes, then sketch it. Sketch the piecewise function. by hand. Decide if it has an inverse function. y x

6 A analytical/ Algebraically To verify two functions, f and g, are inverses of each other, find f(g(x)) and g(f(x)). If both compositions = x for every x in the domain of the inner function, then they are inverses. Example Verify algebraically that the functions are inverses of each other. Finding Inverse Functions Algebraically 1. In the equation, replace f (x) with y. 2. Switch x and y 3. Solve for the new y. 4. Replace the new y with f 1 (x). Example Find f 1 of f(x)= 4x 5 6

7 strategy, first make an input output table for g (x). Then make an input output table for the inverse. x y x y

8 The test is on block day Thursday Sept. 13th or 14th. Any homework that is turned in before Thursday can still get full credit (with the green or yellow late pass) IF you do not have a late pass, you still get 80% for a completed assignment. After the test the homework receives 60% Any student who does not have at least 75% homework (that does not look like it has been copied from BoB or calcchat). Can not retake the test. If a student has not gone to tutor room and or access for help before the test they can not retake the test. In other words if I am not convinced you genuinely tried to prepare and study the first time, you will not get a second time P67 (15 18, 25 31odd, odd, odd 93 99) * no steps = no credit. Do CU Succeed steps #1 and #2 p match the graph and its inverse, only need to show algebraically, (no steps no credit) odd, odd, odd, 115, Chapter 1 Review Worksheet at least 1/3 finished teacher note: 8