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
Assignment: 11.6 on p. 607: 1-21 odds
Assignment: 8.2 Task + RSG
Monday, 15 May 2017
Their area or surface area ratios will be
Their volumes will be in the ratio
Assignment: 11.5 on p. 595: 1-6, 10-17
They should understand how and why the formula works. And also see the relationship between the distance formula and the pythagorean theorem which it is based on
a triangle is right if and only if (its sides a, b and c) satisfy
Assignment: 8.1 Task + RSG