2. Refer to the function p(x) = x². (a) Suppose r(x) = p(x+3) – 2. Describe how p(x) is transformed to create r(x). Verify your description by graphing using Desmos.

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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2. Refer to the function p(x) = x².
(a) Suppose r(x) = p(x+3)– 2. Describe how p(x) is transformed to create r(x). Verify your description
by graphing using Desmos.
(b) Suppose q(x) = -p(x – 1) + 7. Describe how p(x) is transformed to create q(x). Verify your
description by graphing using Desmos.
|
(c) Suppose s(x) = -4p(3(x – 1)) – 2. Describe how p(x) is transformed to create s(x). Verify your
description by graphing using Desmos.
(d) Suppose u(x) is created by shifting p(x) 3 units to the left and 2 units down. Write u(x) in terms of
p(x), and then find an algebraic expression for u(x).
(e) Suppose v(x) is created by compressing p(x) horizontally by a factor of 2 and shifting 9 units up.
Write v(x) in terms of p(x), and then find an algebraic expression for v(x).
Transcribed Image Text:2. Refer to the function p(x) = x². (a) Suppose r(x) = p(x+3)– 2. Describe how p(x) is transformed to create r(x). Verify your description by graphing using Desmos. (b) Suppose q(x) = -p(x – 1) + 7. Describe how p(x) is transformed to create q(x). Verify your description by graphing using Desmos. | (c) Suppose s(x) = -4p(3(x – 1)) – 2. Describe how p(x) is transformed to create s(x). Verify your description by graphing using Desmos. (d) Suppose u(x) is created by shifting p(x) 3 units to the left and 2 units down. Write u(x) in terms of p(x), and then find an algebraic expression for u(x). (e) Suppose v(x) is created by compressing p(x) horizontally by a factor of 2 and shifting 9 units up. Write v(x) in terms of p(x), and then find an algebraic expression for v(x).
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