# Thursday, May 18

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

Today's class. Review of 8.3 distance problems, graphing video activity, no hw.

# 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, May 16

In class we reviewed various forms of conics (ellipses, hyperbola, parabola) and learned about the general form of a quadratic

$\dpi{300}\inline Ax^2 + bxy + Cy^2 + Dx + Ey + F = 0$

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

In class: I checked 11.3 and 11.4 homework, we completed a proof relating to parallel lines and proportional lengths

Assignment: 11.6 on p. 607: 1-21 odds

# Tuesday, May 16

In class many students were absent due to WEB training. We worked in groups to complete 8.2 Task + RSG.

# Monday, May 15

In class topic: ratios between similar figures. If $\dpi{300}\inline a$ and $\dpi{300}\inline b$ are the lengths of two corresponding dimensions between two similar figures, then we can say that all corresponding side lengths will be in the ratio

$\dpi{300}\inline \dfrac{a}{b}$

Their area or surface area ratios will be

$\dpi{300}\inline \left(\dfrac{a}{b}\right)^2 = \dfrac{a^2}{b^2}$

Their volumes will be in the ratio

$\dpi{300}\inline \left(\dfrac{a}{b}\right)^3 = \dfrac{a^3}{b^3}$

Assignment: 11.5 on p. 595: 1-6, 10-17

# Monday, May 15

In class students worked through problems intended to help them create the distance formula

$\dpi{300}\inline d^2 = (x_1 - x_2)^2 + (y_1 - y_2)^2$

which becomes

$\dpi{300}\inline d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

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 $\dpi{300}\inline a^2 + b^2 = c^2$