Thursday, 25 May 2017
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
Students took the Similarity test (chapter 11) on Friday. This week we have learned the right-triangle definition of the trigonometric functions sine, cosine and tangent. As of now these functions take as input one of the non-right angles in a right triangle and their output is a specific ratio of sides in all such similar right triangles.
So, based on this definition, if that means that in any right triangle with a angle, the ratio of is approximately .57. In the figure below this means that .
Monday: No HW
Tuesday: 12.1 on p. 620-624: 4-9, 14-22, 27
1. "Understanding sine/cosine/tangent and their inverses" w/s
2. (3rd Period) 12.1 worksheet
2. (5th Period) 12.2 worksheet
* The distance formula (section 8.1)
* Using coordinates to prove that segments are congruent, parallel or perpendicular (8.2)
* Using congruence, perpendicularity and parallel properties to justify conjectures about shapes. (8.3)
* Writing and analyzing vertical shifts in linear or exponential functions (these have the form f(x) = g(x) + k).
Friday — 8.4 Task + Go (in class) completed on whiteboards, not necessarily in notebook.
Monday — 8.5 Task + RSG
Tuesday — 8.6 Task (Part 1/2/3 all) + 8.6 Set
Today’s assignment: Algebra & Geometry Review worksheet
Thursday, 18 May 2017
In class we spent time reviewing for tomorrow’s Similarity (Ch. 11) Test.
Assignment: Chapter 11 Review on p. 624: 1-21 (pick 12 problems) & be ready for your test tomorrow.
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.
Wednesday, 17 May 2017
In class problem solving to prepare for Friday’s test on Similarity (Ch. 11).
Assignment: Challenge Problems + 11.5/11.6 PYS worksheet.
These problems deal with proving congruence, perpendicularity, and parallelism using coordinate relationships. So for example, showing that the shape below is a rectangle by demonstrating that the slope of each pair of adjacent sides is perpendicular. We demonstrate perpendicularity by computing the slopes of the lines say slope(BC) = -(2/6) = -1/3 and the slope(AB) = 3/1 = 3. Since -1/3 and 3 are negative reciprocals we can see that sides AB and BC are perpendicular, and thus the angle at B is a right angle.
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