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HOMEWORK I : RIGID TRANSFORMATION 1 2 Plot the Parent Function and graph the required transformation. Make sure to label at least 3 points on the final graph. a. 𝑓(𝑥) = √−𝑥 + 2 − 1 b.𝑓(𝑥) = − (𝑥 − 2)3 + 3 3. The graph of 𝑦 = 𝑓(𝑥) passes through the given points (0,1) , (1,2) and (2,3). Find the corresponding points on the graph of: c. 𝑓(𝑥) = −(𝑥 − 3)2 − 2 4. The graph of ℎ(𝑥) passes through ( -4,2). Find the corresponding point on the graph of: a. 𝑦 = −2ℎ(𝑥 + 1 ) − 3 a. 𝑦 = −𝑓(𝑥 + 2) − 1 b. 𝑦 = 𝑓(2 − 𝑥) + 3 b. 𝑦 = −ℎ(2𝑥 − 1) + 1 c. 𝑦 = −𝑓(−𝑥 − 1) − 5 5. Name the Parent and describe all its transformations. Do not graph: a. 𝑓(𝑥) = − √−𝑥 + 1 + 3 6. Given a description of its transformation, give the new equation. a. 𝑃𝐹: √𝑥 , reflection across the x-axis, shift 3 units left and 2 units up, reflects across the y-axis. b. ℎ(𝑥) = |1 − 𝑥| − 4 b. 𝑃𝐹: 𝑥 3 , shift 3 unit right and 1 unit down, reflects across the y-axis. 3 HW 2 NONRIGID TRANSFORMATION: A. Describe all the transformation in each of the following functions( Identify each Parent Function. 1. ℎ(𝑥) = 2 log(−𝑥 + 3) − 5 B. Find the function that is finally graphed after the following transformations are applied to the given parent function (PF) 6. PF: 𝑦 = log 𝑥 5. PF : 𝑦 = 3√𝑥 1 2 𝑓(𝑥) = − 2 (𝑥 − 4)3 + 1 3. 𝑝(𝑥) = −√10 − 2𝑥 − 3 3 …Shift 3 units left …Shift 2 units up …Vertically compressed by a factor of ½ …reflects across x-axis …reflects across y-axis …Shift 1 unit left …Shift 4 units down …Horizontally stretched by a factor of 4 …Reflects across y-axis …Vert. stretched by 3 7. PF: 𝑦 = 𝑒 𝑥 8. PF: 𝑦 = |𝑥| …Hor. Stretched by 3 …Shift 1 unit down …shift right 1 unit …Vert. comp. by 1/3 …Reflects across y-axis …reflects across x-axis …Vertically stretch by a factor of 2 …Horizontally comressed by a factor of ½ …Reflects across y-axis …Shift 2 units up …Shift 1 left 4. 𝑣(𝑥) = −2 √( 5 − 𝑥) − 6 5. ℎ(𝑥) = 0.2 |−3𝑥 − 6| + 1 9. If (-8,6) is on the graph of 𝑦 = ℎ(𝑥), what is the corresponding point on the graph of 1 𝑎) 𝑦 = − 2 ℎ(3 − 2𝑥)+1? 1 b) 𝑦 = 3ℎ (− 2 (𝑥 − 1)) − 3? 1 c)𝑦 = 3 ℎ(−3𝑥 + 6) − 2 10. Plot the PF and sketch according to the required transformation. Clearly label at least 3 points of the final graph. 3 1 1 𝑏. 𝑓(𝑥) = 2 √𝑥 + 1 − 3 𝑐. ℎ(𝑥) = − |6 − 3𝑥| + 1 (𝑥 a. ℎ(𝑥) = −3 √− 2 − 1) + 4 2 2 d. 𝑓(𝑥) = − 𝑥+1 − 3 1 e. ℎ(𝑥) = −2 |2 (𝑥 − 6)| + 1 𝑓. ℎ(𝑥) = −2 (3 − 𝑥)2 − 1 Classwork NON-RIGID TRANSFORMATION CLASSWORK ( Please make a copy of this before our class) on October 15, 2020 (A Day) and October 16 (B Day) A B C D E F D 1 *** Given that points (-6,-4) and (9,2) are on f(x), what is the new coordinate of 𝑦 = − 2 𝑓( 12 − 3𝑥) + 1?