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.
Thursday, May 18
Wednesday, 17 May 2017
Wednesday, May 17
In class problem solving to prepare for Friday’s test on Similarity (Ch. 11).
Assignment: Challenge Problems + 11.5/11.6 PYS worksheet.
Wednesday, May 17
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
Tuesday, May 16
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
Tuesday, May 16
Assignment: 11.6 on p. 607: 1-21 odds
Tuesday, May 16
Assignment: 8.2 Task + RSG
Monday, 15 May 2017
Monday, May 15
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
Monday, May 15
which becomes
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