cherylim23's methods question thread :)

[|ll|lll|]

Hi, I don't understand why y is halved and x remains the same when y = x^3 is dilated by a factor of half from the x-axis.
Got that from heinemann textbook.

[the.watchman]

The process of dilating by a factor of 'k' from the y-axis is replacing x with

So, in this case,

[|ll|lll|]

Oops, sorry. I meant x-axis.
The qn stated: What happens to the ht and width of this portion of the slide if the function is dilated by a factor of 1r2
The ht supposedly was halved and the width stays the same.

[the.watchman]

So, for dilation by 1/2 from x-axis, y should be replaced by y/(1/2)=2y

If it helps, draw the old and new graphs and compare them
The new graph should look squished vertically, but it can be interpreted as a stretch horizontally as well

[|ll|lll|]

Yeah, I did them on my CAS. However, for the original one, it has a y-intercept at (0,12). After dilation, the y-intercept is  (0,10).
(Graphs are: -4r125 (x-5)^3 + 8 and -2r125 (x-5)^3 + 8

[the.watchman]

Yeah, I did them on my CAS. However, for the original one, it has a y-intercept at (0,12). After dilation, the y-intercept is  (0,10).
(Graphs are: -4r125 (x-5)^3 + 8 and -2r125 (x-5)^3 + 8

In this case, the intercept is affected by the translation (up 8 units) AFTER the dilation, so the intercept does not double

[|ll|lll|]

So the answer is probably wrong? You mean the height (y intercept) decreases but the width stays the same?
I'm not too sure about the width either...

[the.watchman]

I don't think you understood what I meant
There is a translation up eight units, so the 'new' line from which the dilations occur is y=8
Considering that, isn't the second intercept double the first, if you are talking about the distance from the line y=8?

[|ll|lll|]

Oh yeah, I get what you mean
However, for the question, i think the dilation was after the translation...
Oh well, nevermind. I have another question

For y=(x-a)^3(x-b), where a and b > 0,
as x approaches infinity, y approaches infinity. (i.e. x --> i, y --> i)

how about, when x approaches negative infinity, what happens to y? (i.e. x --> -i, y --> ?)

Also, the y-intercept is at a^3b right?

[the.watchman]

Considering the type of graph, it is a positive quartic (power 4, positive co-efficient)
So as

[brightsky]

For y=(x-a)^3(x-b), where a and b > 0,
Also, the y-intercept is at a^3b right?

Yep.

[|ll|lll|]

Considering the type of graph, it is a positive quartic (power 4, positive co-efficient)
So as

okay, so you just ignore the minimum part where x < 0?

[the.watchman]

Considering the type of graph, it is a positive quartic (power 4, positive co-efficient)
So as

okay, so you just ignore the minimum part where x < 0?

What do you mean?

Another way to work it out is to think of the y-value, if you let x be a very big number

[brightsky]

Considering the type of graph, it is a positive quartic (power 4, positive co-efficient)
So as

okay, so you just ignore the minimum part where x < 0?

You can also think of it this way.



If you substitute in , in other words, a very big negative number, then would be a very big negative number and would also be a very big negative number.

Now as for , when you substitute in x as a very big negative number, would also be a very big negative number.

Now the equation turns out to be





Hope this helps.

[|ll|lll|]

Yeah, thanks.
I understand both replies.
But if you plot the graph, between a < x < b (assuming b > a), y decreases instead of increasing.
So do I just ignore the part for a < x < b?