Re: why doesn't the range on this interval match the plot range?

• To: mathgroup at smc.vnet.net
• Subject: [mg66431] Re: why doesn't the range on this interval match the plot range?
• Date: Fri, 12 May 2006 02:03:15 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```On 5/11/06 at 2:15 AM, chris at chiasson.name (Chris Chiasson) wrote:

>Parabola[x_]=4x^2+53x+160
>BeginPoint=-8;
>EndPoint=-5;
>Plot[Parabola[x],{x,BeginPoint,EndPoint}]
>Parabola[Interval[{BeginPoint,EndPoint}]]

Because Mathematica substitutes the entire interval for x to your function not just the interval end points. That is

In[26]:=
a=4Interval[{-8,-5}]^2

Out[26]=
Interval[{100,256}]

Note because of the minus sign, the result of Interval[{(-8}^2,(-5)^2}] is
Interval[{5^2, 8^2}]. That is for the first term, the end points are in "reverse" order from what you are expecting.

In[27]:=
b=53Interval[{-8,-5}]

Out[27]=
Interval[{-424,-265}]

In[28]:=
a+b+160

Out[28]=
Interval[{-164,151}]

while

In[29]:=
4x^2+53 x+160/.x\[Rule]-5

Out[29]=
-5

and

In[30]:=
4x^2+53 x+160/.x\[Rule]-8

Out[30]=
-8
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