Lesson 5- Combining Transformations of Functions 1. Describe what happens to the graph of a function if the following changes are made. a) Replace x with x +4, and y with-y There is a tronslation lett 4, and a relleclion in the x-axis b) Replace x with 2x, and y with y +3 down3 There is a hori 2ontal compre ssion by 1/2 and translotion c) Replace x with -x and y with-y, then replace x with x-3 There is a horizontal expansion bu 3 and a rettection in the 1 C then, a translation right 3 d) Replace x with-3x then y with 2y, then replace x with x+1 and y with y-6 There is a horizontal com0vession by 113 and a retle clion in the y then a yevlical compsession by 12, then a translatign lelt ,ano 2. Consider the function y = f(x). 'Show the results of each transformation in the order given and finish by simplifying so each new equation begins with y=. a) a horizontal expansion by 3, then a translation 2 units left b) a vertical expansion by 2, a reflection in the x-axis, and a translation 3 units down. c) a horizontal compression by , a reflection in the y-axis, then a translation 4 units right and 2 units up. d) a vertical compression by , a horizontal compression by , a reflection in the x-axis, then a translation 7 units left and 6 units down.
Lesson 5- Combining Transformations of Functions 1. Describe what happens to the graph of a function if the following changes are made. a) Replace x with x +4, and y with-y There is a tronslation lett 4, and a relleclion in the x-axis b) Replace x with 2x, and y with y +3 down3 There is a hori 2ontal compre ssion by 1/2 and translotion c) Replace x with -x and y with-y, then replace x with x-3 There is a horizontal expansion bu 3 and a rettection in the 1 C then, a translation right 3 d) Replace x with-3x then y with 2y, then replace x with x+1 and y with y-6 There is a horizontal com0vession by 113 and a retle clion in the y then a yevlical compsession by 12, then a translatign lelt ,ano 2. Consider the function y = f(x). 'Show the results of each transformation in the order given and finish by simplifying so each new equation begins with y=. a) a horizontal expansion by 3, then a translation 2 units left b) a vertical expansion by 2, a reflection in the x-axis, and a translation 3 units down. c) a horizontal compression by , a reflection in the y-axis, then a translation 4 units right and 2 units up. d) a vertical compression by , a horizontal compression by , a reflection in the x-axis, then a translation 7 units left and 6 units down.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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