Question

Can someone help me understand this?

Answer 1

Given the function k(x) = x2, compare and contrast how the application of a constant, c, affects the graph. The application of the constant must be discussed in the following manners:
k(x + c)
k(x) + c
k(cx)
c • k(x)

Answer 2

results could be shifting, stretching etc. depending on how you use c

Answer 3

I know absolutely nothing on how it works. When they were teaching me...i did not see it like this

Answer 4

\(\large \begin{array}{llll}
k(x) = x^2\\ \quad \\ \quad \\
k(x + c)\implies &(x+c)^2\\
k(x) + c\implies &x^2+c\\
k(cx)\implies (cx)^2\implies &c^2\cdot x^2\\
c \cdot k(x)\implies &c\cdot x^2

\end{array}\)

Answer 5

y = A ( Bx + C ) + D

A = stretch/expand the graph by a factor A
B = stretch/expand the graph by a factor B
C = horizontal shift
D = vertical shift

Answer 6

http://www.youtube.com/watch?v=5oQgzup9nx4

Answer 7

is there another way It can be explained?

Answer 8

@Hero Are you familiar with this?

Answer 9

well, the video shows pretty much what happens, is very straightforward once you have the "parent function"

Answer 10

Would you understand it better if it were \(f(x) = x^2\) ?

Answer 11

Yes!

Answer 12

\(\large \begin{array}{llll}
f(x) = x^2\\ \quad \\ \quad \\
f(x + c)\implies &(x+c)^2\\
f(x) + c\implies &x^2+c\\
f(cx)\implies (cx)^2\implies &c^2\cdot x^2\\
c \cdot f(x)\implies &c\cdot x^2

\end{array}
\)

Answer 13

Like for example

\(c \dot\ f(x) = c \dot\ x^2\)

\(c\) being a number multiplied by \(f(x)\)

\(f(x)\) and \(x^2\) are inter-changable in this case.

Answer 14

@jdoe0001 is quick

Answer 15

So the whole compare and contrast is basically the answers to each one

Answer 16

it helps using an editor /me ducks

Answer 17

=)

Answer 18

What editor?

Answer 19

@crystelle, you have to graph each equation to understand the differences between their graphs.

Answer 20

In every case, the graphs are simply transformation of the parent function \(f(x) = x^2\)

Answer 21

Alrighty. and this is for what? y = A ( Bx + C ) + D

A = stretch/expand the graph by a factor A
B = stretch/expand the graph by a factor B
C = horizontal shift
D = vertical shift

Answer 22

You have to be careful with using that A, B, C, D stuff. It's better to understand this concept in terms of transformations of \(f(x)\)

Answer 23

Alright gotcha. and the problems jdoe gave me is what I put as my answer next to those problems? showing thats how you really solve them?

Answer 24

The question asked you to compare and contrast the graphs of those transformations. You still have to graph them and describe similarities and differences of the transformation with respect to the parent function f(x). Good luck with it.

Answer 25

yeah im gonna do it...how exactly do i graph..with no numbers?

Answer 26

What you do is use an arbitrary number. Try c = 5 and then graph. Just say, for example, if c = 5, then we have the following graphs:

f(x) = x^2
g(x) = (x + 5)^2
h(x) = 5x^2
j(x) = x^2 + 5
k(x) = 25x^2

Then from there you can begin comparing

Answer 27

https://www.desmos.com/calculator/azxiramsbu

Answer 28

so I can make up my own number? ok good
can u save a graph file on that site?

Answer 29

You could still do that on paper, except you could pretend the 5 is a c

Answer 30

If you wanted to get creative with it, you could use letters instead of numbers. for example

a = 1
b = 2
c = 3
0 = 0
-a = -1
-b = -2
-c = -3

Answer 31

So your axes could look something like this: