vertical and horizontal shifts, answer provided - just need to understand method :)

[christinawiler]

I have the answer from the back of the book on these but have no idea how they get to that point. Any help is greatly appreciated!

Write a formula and graph the transformations of m(n) = (1/2)n^2

1. y = m(n+1)
2. y = m(n-3.7)

Answers:
1. (1/2)n^2 + n + (1/2)
2. (1/2)n^2 - 3.7n + 6.845

Thank you!!

 

[Deleted member 4993]

I have the answer from the back of the book on these but have no idea how they get to that point. Any help is greatly appreciated!

Write a formula and graph the transformations of m(n) = (1/2)n^2

1. y = m(n+1)
2. y = m(n-3.7)

Answers:
1. (1/2)n^2 + n + (1/2)
2. (1/2)n^2 - 3.7n + 6.845

Thank you!!

For #1, replace n by (n+1) in 1/2 * n^2

thus

m(n+1) = 1/2 * (n+1)^2 .... now expand the right-hand-side to get the correct form

Now try #2 following the same logic.....

 

[christinawiler]

For #1, replace n by (n+1) in 1/2 * n^2

thus

m(n+1) = 1/2 * (n+1)^2 .... now expand the right-hand-side to get the correct form

Now try #2 following the same logic.....

Thank you so much!!!!

 

[soroban]

Hello, christinawiler!

I found the notation confusing.
Why did they use \(\displaystyle m\) for the function and \(\displaystyle n\) for the variable?

Write a formula and graph the transformations of \(\displaystyle f(x) \,=\,\frac{1}{2}x^2\)

. . \(\displaystyle 1.\;\;y \,=\, f(x+1) \qquad 2.\;\; y\,=\,f(x-3.7)\)

Isn't that easier to read?