Unit 4 Advanced Functions Review Day
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1 Unit 4 Advanced Functions Review Day
2 Warm-up! Find the domain and range of the following functions. Then, tell how they are changed from their parent graph. (Hint: Remember that the order of transformations can be important) f ( x) 2 x f( x) 4 x 3 1) 2) Change #1 to -> this one!! f ( x) 9x ) 4) f x 3 ( ) 8x 16 5 f ( x) 3 x 7 1 5) Write a Piecewise Function for the graph shown. Then tell its domain and range. (Hint: use graph paper!) Warm-Up continues on next slide!
3 Warm-up CONTINUED! Released Exam problems 6. The amount of time it takes to build a road varies inversely with the number of workers building the road. Suppose it takes 50 workers 8 months to build the road. Write an equation that could be used to determine how long it would take n workers to build the road. (Be sure to define the variables. How much faster would 60 workers build the road than 50 workers? 7. The force, F, acting on a charged object varies inversely to the square of its distance, r, from another charged object. When the two objects are 0.64 meters apart, the force acting on them is 8.2 Newtons. Approximately how much force would the object feel if it is at a distance of 0.77 meters from another object? Round to the tenths place. Warm-Up continues on next slide!
4 Warm-up CONTINUED! Given f(x) = x 2 3x + 2, find 8. f(x 4) 9. f(x + 2) 3f(x)
5 Warm-Up Solutions Find the domain and range of the following functions. Then, tell how they are changed from their parent graph. (Hint: Remember that the order of transformations can be important) f ( x) 2 x f( x) 4 x 3 1) 2) Domain: Range: (, 3) ( 3, ) (, 4) ( 4, ) Vertical Stretch by 2, left 3, down 4 3) 4) f x Domain: Range: 3 ( ) 8x 16 5 Vertical Stretch by 2, right 2, down 5 f ( x) 9x 54 2 f ( x) 3 x 7 1 Domain: [ 6, ) Domain: (, ) Range: (,2] Range: (,1] Reflected over x-axis, Vertical Stretch by 3, left 6, up 2 (, ) (, ) Reflected over x-axis, Vertical Stretch by 3, right 7, up 1
6 Warm-Up Solutions 5) Write a Piecewise Function for the graph shown. Then tell its domain and range. (Hint: use graph paper!) Domain: (, ) Range: (, ) 2 x 4 if x 1 F( x) { 2 x 1 if x 1
7 Warm-up ANSWERS! Add these Released Exam problems in to your notes!! 6. The amount of time it takes to build a road varies inversely with the number of workers building the road. Suppose it takes 50 workers 8 months to build the road. Write an equation that could be used to determine how long it would take n workers to build the road. (Be sure to define the variables. How much faster would 60 workers build the road than 50 workers? t = k where t = time in months, and n n = # people working to build the road 8 = k 50 t = 400 = 6 2/3 months 60 for 60 workers 400 = k t = 400 n t = 8 months 6 2/3 months = 1 1/3 months faster!!
8 Warm-up CONTINUED! Add these Released Exam problems in to your notes!! 7. The force, F, acting on a charged object varies inversely to the square of its distance, r, from another charged object. When the two objects are 0.64 meters apart, the force acting on them is 8.2 Newtons. Approximately how much force would the object feel if it is at a distance of 0.77 meters from another object? Round to the tenths place. F = k r 2 where F = force acting on a charged object, r = distance from another charged object 8.2 = k (0.64) 2 k = (8.2) (0.64) 2 = F = r 2 F = (0.77) 2 = Force on object at a distance 0.77 m from object F ~ 5.7 Newtons
9 Warm-up CONTINUED! Given f(x) = x 2 3x + 2, find 8. f(x 4) x 2 11x f(x + 2) 3f(x) -2x x - 6
10 HW Answers (some work is shown on later slides) v 2. r x 6, 3 4. x 1 9. LCD : m 9 Answer : m LCD : ( x 4)( x 4) Answer : x n 6. r 4, x 8. a LCD : ( x 11)( x 6) Answer : x LCD : ( x 7)( x 3) 1 Answer : x LCD : 3( w 4) Answer : w 10
11 HW Piecewise Review Answers 14. For the following function g, decide if each of the statements is true or false. If it is false, fix the equation or restriction. A C B E D F 1. The range of this function is [ 2, ) F, { 2} [0, ) 2. The equation for the line from point A to B is g( x) 2x F, g( x) x 3. From C to D the equation is g(x) = -2 True 4. The restriction from C to D is 0 x 5 F, 0 x 4 5. The equation for E to F is g( x) x 4 F, g( x) x 4
12 HW Answers Work v 2. r x 6, 3 4. x 1
13 HW Answers Work = -17 3
14 HW Answers Work
15 HW Answers Work
16 HW Answers Work
17 Tonight s Homework Packet page (updates on next slide) Remember To Study For Your Test Tomorrow!! Suggestion Of The Day: Use website, notes, Unit 4 Quiz 1 & 2, mini quizzes, and homework packet to help you study!! Tomorrow Night s Post-Test Homework Packet p AND Print next packet
18 Packet update For tomorrow Night s Test Review Homework Packet p There are some updates to Packet p y = -2 x - 1 AND Omit #5, 9, 13
19 Jeopardy Review! Advanced Functions Practice Grab a whiteboard, marker, and eraser!
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