During class we discussed more about blogging. This years AP Calculus class has gotten off to a great start. Mr. K. talked about Scribe Post Hall of Fame (http://thescribepost.pbwiki.com). Which is a page of the best scribe posts throughout the entire history of this website. I believe the Applied class last year was in it 12 times in a row. Our class can surely accomplish that, no problem. :) Well, just remember to post up comments on how the posts should be inducted into the Hall of Fame. The students should judge; "It looks good, but did I learn?"
Okay down to business, the following questions are the problems we solved today:
#1) If f(x)=√(x2+8)
a) Find domain of f(x)
First let's see what we basically know: Remember you can not square root negative numbers! Aslo, when graphing f(x) it is a parabola opening upwards. So let us check if this function has x-intercepts:
b) Write a formula for the function whose graph is the reflection of f(x) across the y-axis.
So only the x-coordinates change.
c) Write a formula for the function obtained by shifting f(x) 3 units right, flipping the graph over the x-axis, and then shifting it up 4 units.
This question contains three transformations:
Horizontal Shift: f(x-3)=√((x-3)2+8(x-3))
Reflection of y-axis: f(x-3)=-√((x-3)2+8(x-3))
Vertical Shift: f(x-3)+4= - √((x-3)2+8(x-3))+4
#2) "In Winnipeg at 5:00, headed for Gimli, a distance of 60 miles. Due to an accident on the highway, traffic was creeping along for the first hour and a half. By 6:30 we were only 20 minutes from Gimli. After that we were able to speed up gradually and finally reached Gimli at 7:30."
a) Draw a possible graph to represent the distance in miles from Winnipeg, as a function of time, in hours since 5:00.
b) Explain the important features of your graph, including commonts on concavity.
At the beginnig the car travels at a constant speed while in traffic, the car then speeds up as it is freed from traffic, then it slows down as it comes closer to reaching it's destination.
Near the end is where concave downward happens; it bends down.
We also completed the question we started on September 9.
We found out that f(x) is an exponential function.
Here are the instructions for solving this problem on your graphic calculator:
- STAT, Edit, Now fill in the table. *Make sure to ClrAllLists*
- 2nd STAT PLOT, Plot1 on, on, scatter plot
- ZOOM 9 (ZoomStat)2nd QUIT, STAT CALC 0, ExpReg, L1, L2, Y1, ENTER
- If r2 or r (corolation of coefficient) doesn't show up press:2nd 0 (CATALOG), DiagnosticOn, ENTER, then go back
Therefore f(x) is an exponential function.
HOMEWORK: 1.3 odd numbers and question 2
*Well I hope this helped everyone. Please do not hesitate to post comments about any mistakes that I've made.*
This was a bit difficult, since I'm computer-illeterate. But I guess I did okay, did my best. Alright who shall I choose... hmmmm.... are next scriber is LINGER! 8D