Need some help with functions.

Test Preparation AP Test Preparation
1

<p>Hi,</p>

<p>I’m finishing up some calculus ab hw and I need some help.
Just a couple questions:</p>

<li>Given f(x)= [x-3]+[x]-6
Find all roots to the nearest 0.001
( [x] is the IntegerPart of x. )</li>
</ol>

<p>I can’t seem to get the roots using the TI-89 Titanium.
Using the zeros function, I get back {} as the answer. </p>

<li>f(x) = 2x + 3
Sketch the graph of [f(x)]
How do I do this?
I’m kind of confused. Do I just graph
f(x) = [2x+3]? Isn’t it [f(x)]= 2x + 3?</li>
</ol>

<p>Any help would be much appreciated.
Thanks.</p>

2

<h1>1 Perhaps there are no roots?</h1>

<h1>2 [f(x)] = [2x + 3]. That is what you graph</h1>

3

<h1>1: [x-3] + [x] - 6 = [x] - 3 + [x] - 6 = 2[x] - 9.</h1>

<p>Now 2[x] - 9 = 0, only when 2[x] = 9, or when [x] = 9/2. Since [x] is an integer, [x] = 9/2 is always false.</p>

<p>The key to this problem is recognizing that [x-3] = [x]-3, and in fact [x-a] = [x]-a for all integer values of a.</p>