Question

Hey guys. Can you help me clarify something?

In these situations:

f(x+c)
f(x)+c
f(cx)
c*(fx)

When you add a constant, like 2 to it, what would happen to the graphs?

Answer 1

You just take all of them and add 2?
It would add 2 therefore to all possible values returned by the function, and if you graph it, it would be all shifted by 2 points up.
Is that what you meant?

Answer 2

I mean like when c=2

Answer 3

I see, ok sec

Answer 4

\(\bf \textit{say let us use this for example}\quad x^2\\ \quad \\
f(x+c)\implies (x+c)^2\\
f(x)+c\implies x^2+c\\
f(cx)\implies (cx)^2\implies c^2x^2\\
c\times(fx)\implies cx^2\)


recall that

y = A ( Bx + C ) + D

A = vertical expand/shrink by A factor
B = vertical expand/shrink by B factor
C = horizontal shift, C > 0, to the left, C < 0, to the right
D = vertical shift, D > 0, up, D < 0, down

Answer 5

Alright. What happens when c=2?

Answer 6

\(\bf f(x+2)\implies (x+2)^2\\
f(x)+2\implies x^2+2\\
f(2x)\implies (2x)^2\implies 2^2x^2\\
2\times(fx)\implies 2x^2
\)

Answer 7

you just need to keep in mind that, all those SHIFTS or TRANSLATIONS or TRANSFORMATIONS are just PADDED STUFF to the original parent function

so is really just the parent function, with PADDED stuff around it

Answer 8

and the PADDING, makes the graph move about or expand or shrink

Answer 9

I see, I see

Answer 10

So will it move up two places or over two and all that jazz?

Answer 11

yeap

Answer 12

like say somthing like \(\bf 2(x-3)^2+5\) what that will do is, take \(\bf x^2\) and shrink it vertically by factor of "2", shift it to the right by "3" units and shift it downwards vertically by "5" units

Answer 13

woops, shift it UPWARDS rather, is a + 5, so up by 5 units
and so on

Answer 14

Thanks! :))

Answer 15

yw