Assignment: 9.8 on p. 555: 1-8, 11-12
Here is an example problem, similar to the one worked in class.
Let's analyze the function given by the equation below. We will try to work out its various characteristics and sketch a graph before resorting to computer graphing.
To obtain a common denominator we multiply the first term by and the second term by
Now we can simplify the expressions in the numerators and re-write as a single fraction.
Which simplifies to
Now that the function is in rational form, we can analyze its properties.
The function has vertical asymptotes at
We can tell from the numerator that the function will have x-intercepts where the numerator evaluates to zero, so we solve to get
So, we note the two x-intercepts.
In addition, we note that this function has denominator of greater degree than the numerator, so as approaches the denominator will overpower the numerator and the value of the function will approach , creating horizontal asymptotes at
Through point testing and some more intuition we can identify the location of the 4 sections of this function and sketch a graph
Thursday, 18 May 2017
In class: we studied the definition of /rational functions/ and looked at the graph of f(x) = 1/x and transformations of this parent function.
For example the function f(x) = 1/x
When transformed to g(x) = 3/(x-4) + 1 incurs a vertical stretch by factor 3 and horizontal shift of +4 to the right and vertical shift + 1. The asymptotes of the function are transformed with the function, so the asymptotes y = 0 and x = 0 of the parent function are vertically stretched (no effect) then vertically shifted (y -> 3fy + 1) and horizontally translated (x -> x + 4), so the x = 0 vertical asymptote moves right to x = 4.
Also, our nice point (1,1) moves 4 to the right and takes a vertical stretch by factor 3 followed by a vertical shift + 1, so (1 + 4, 1*3+1) = (5, 4)
Assignment: 9.6 on p. 536: 1-8, 10-12
Reminder: SBAC testing in Ms. Mac’s room tomorrow during 6th period.
Tuesday, 16 May 2017
Today's problems ask students to convert between this general form and the standard form of various other conic sections.
Assignment: 9.5 on p. 531: 1-8, 10, 13-16
Monday, 8 May 2017
Assignment: Read 9.3 and complete 1-9 on p. 511.
Tuesday, 2 May 2017
9.1 on p. 491: 1-5, 6-12 evens
9.2: on p. 503: 1-5 (skip 4) and 11
Thursday, 27 April 2017
1) Chapter 8 Review on p. 483: complete 1-11
2) Graded Problem write-up
Smart Pilot, MYP Criteria D Problem Write Up
- Question: How would a pilot plot a rudimentary course between two points using trigonometry to determine the correct bearing and flight duration?
- Find two cities and determine the distance and bearing from one to the other (as the crow flies)
- Find the airspeed of a plane
- Find a wind speed and bearing that you think would be reasonable (may not be in a nice line with your plane)
- Determine the bearing which the pilot should follow, the duration of the flight
- Present your work and explanation [Graded on Criteria D] Due on Tuesday
Tuesday, 25 April 2017
Assignment: 8.7 on p. 480: 1-7, 11-14 + 8.7 practice problems from packet.
Saturday, 22 April 2017
1) 8.6 on p. 472: 1-9, 15
2) Read 8.7 on Law of Cosines
3) Complete 8.5/8.6 practice problems from packet
Tuesday, 18 April 2017
1) 8.3/8.4 worksheet
2) 8.5 on p. 464: 2-12 even, 13-16. Also, note that you will need the gravity table on p. 460
3) Read the section before/during or after you complete your assignment
Friday, 14 April 2017
Assignment for Tuesday:8.4 on p. 455: 1-5, 7-9