- #1
|<ings
- 14
- 0
This is just to see if I remember? Please confirm, correct any errors, and answer the questions (q's in bold)
What geometric transformations will "transform"
f(t) = [tex]\frac{mg}{b}[/tex] * (1 - e-bt/m)
= [tex]\frac{mg}{b}[/tex] - [tex]\frac{mg}{b}[/tex])e-bt/m
(1) vertical scaling? or horizontal?
f((-b/m)t) -> e-bt/m
let the new f function be equal to g, another function
i.e. g(t) = e-bt/m
(2) reflection across the x-axis, right?
-1 * g(t) = -e-bt/m
let the new g function be equal to h, another function
i.e. h(t) = -e-bt/m
(3) i think this one is the vertical scaling.
[tex]\frac{mg}{b}[/tex] * h(t) = -[tex]\frac{mg}{b}[/tex]e-bt/m
let the new h function be equal to i, another function
i.e. i(t) = -[tex]\frac{mg}{b}[/tex]e-bt/m
(4) vertical translation
i(t) + [tex]\frac{mg}{b}[/tex] = [tex]\frac{mg}{b}[/tex] - [tex]\frac{mg}{b}[/tex]e-bt/m
= [tex]\frac{mg}{b}[/tex] * (1 - e-bt/m)
= f(t)
also, is the reflection across the y-axis [STRIKE]done by multiplying by -1 inside of the[/STRIKE] done like this?: f(x) [tex]\stackrel{reflection across y-axis}{\rightarrow}[/tex] f(-x). TNX
Homework Statement
What geometric transformations will "transform"
f(t) = et [tex]\stackrel{transformations}{\rightarrow}[/tex] [tex]\frac{mg}{b}[/tex] * (1 - e-bt/m)?
Homework Equations
f(t) = [tex]\frac{mg}{b}[/tex] * (1 - e-bt/m)
= [tex]\frac{mg}{b}[/tex] - [tex]\frac{mg}{b}[/tex])e-bt/m
The Attempt at a Solution
(1) vertical scaling? or horizontal?
f((-b/m)t) -> e-bt/m
let the new f function be equal to g, another function
i.e. g(t) = e-bt/m
(2) reflection across the x-axis, right?
-1 * g(t) = -e-bt/m
let the new g function be equal to h, another function
i.e. h(t) = -e-bt/m
(3) i think this one is the vertical scaling.
[tex]\frac{mg}{b}[/tex] * h(t) = -[tex]\frac{mg}{b}[/tex]e-bt/m
let the new h function be equal to i, another function
i.e. i(t) = -[tex]\frac{mg}{b}[/tex]e-bt/m
(4) vertical translation
i(t) + [tex]\frac{mg}{b}[/tex] = [tex]\frac{mg}{b}[/tex] - [tex]\frac{mg}{b}[/tex]e-bt/m
= [tex]\frac{mg}{b}[/tex] * (1 - e-bt/m)
= f(t)
also, is the reflection across the y-axis [STRIKE]done by multiplying by -1 inside of the[/STRIKE] done like this?: f(x) [tex]\stackrel{reflection across y-axis}{\rightarrow}[/tex] f(-x). TNX
Last edited: