Question

cubic function? help. I'm confused on the shrinking/stretching ):

Answer 1

im gonna post an example D:

Answer 2

\(y=ax^3+bx^2+cx+d\)
if \(|a|>1\) it is a vertical stretch.
if \(0<|a|<1\) then it is a vertical shrink

Answer 3

is your function \(y=2(x-4)^3-1\)?

Answer 4

im not sure about the the 2, bust (x-4)^3-1 i agree with

Answer 5

maybe \(y=\frac{1}{2}(x-4)^3-1 \)

you can determine \(a\) by using a point on the graph.

Answer 6

\[1=a(6-4)^2-1 \Rightarrow 2=4a \Rightarrow a = \frac{1}{2}\]

Answer 7

so it is a ________?

Answer 8

how come it's a(6-4)^2? why is it squared. shouldn't it be cubed?

Answer 9

@pgpilot326

Answer 10

@ganeshie8

Answer 11

@aum

Answer 12

cause you are substituting for a quadratic instead of a cube

Answer 13

Can you type the parent function and the transformed function? It is not clear from the pic which is posted sideways.

Answer 14

ok

Answer 15

parent function is y=x^3
transformed= (answer) is 1/2(x-4)^3-2

Answer 16

!. x in the parent function is replaced by (x-4). This translates the parent function to the RIGHT by 4 units.
2. Then (x-4)^3 is multiplied by 1/2. This reduces or shrinks the y-value by a factor of two. So there is vertical compression to half the original value.
3. Then subtraction of 2 causes a vertical translation DOWN by 2 units.

Answer 17

@aum im doing the reverse way. How would i find the compression/stretch if given the point of (6,-1)?

Answer 18

@aum

Answer 19

how do i do the substitution, cause the guy above substitute the point in a quadratic function. But his answer was correct

Answer 20

Are you given a graph from which you have to find the function?
The link is sideways making it hard to read what is given and what is asked.

Answer 21

type the transformed function into https://www.desmos.com/calculator

Answer 22

yes im given a graph

Answer 23

Can you post the pic upright where it is clear what is given and what is asked?

Answer 24

ok

Answer 25

let me rotate it

Answer 26

oh nevermind

Answer 27

Still I don't see anything that say the parent function is y = x^3.

Answer 28

you have to identify it

Answer 29

it was originally a cubic function, now it's transformed

Answer 30

Okay, it does look like a cubic function shifted to the right.
The flat part of the curve in the graph is at (4,-1)
y = x^3 has the flat part at (0,0)
So this function has been shifted to the right by 4 unit and down by 1 unit. Therefore,
y = (x - 4)^3 - 1.
And ....

Answer 31

We see a point (6, 1) on the graph. That is, when x = 6, y = 1.
Let us see what the equation y = (x - 4)^3 - 1 gives us when x = 6:
y = (6 - 4)^3 - 1 = 8 - 1 = 7.
So the y value instead of being 7 is 1. So there is a vertical compression.
So y = a(x-4)^3 - 1. Where 'a' is the vertical compression/stretch.
Now put x = 6 and y = 1 and solve for a.
1 = a(6 - 4)^3 - 1
1 = 8a - 1
8a = 2
a = 1/4

y = 1/4(x - 4)^3 - 1

Answer 32

\[
\text{Parent function } ~ y = x^3~ \text{ transformed to: }~~y = \frac 14(x-4)^3 - 1
\]

Answer 33

ah, oh the guy above before confused me

Answer 34

ty i understand :D

Answer 35

You are welcome.