Week 7 of m151
(§ 2, Mr. Lane)
6–10 March 2017

Math Learning Center (in Math 011) has tutors:
9am–4pm on Monday–Thursday and 9am–1pm on Friday

math@Mansfield (Library) has tutors: 6:30pm – 9:00pm on Sunday–Thursday

math@Mansfield (Library) has tutors: 6:30pm – 9:00pm on Sunday–Thursday

- Monday (6 March 2017) [d20]
WeBWorK:
RQ-6-3 closes at 10 am
- Study section 6.3
(
*Horizontal Stretches and Combinations of Transformations*).- Let f be the function graphed in Figure 2.22 on page 89;
its domain is interval [0,4) and its range is set {1,2,3,4}.
- Find domain and range of g(x) = f(x/3), then sketch its graph.
- Find domain and range of h(x) = f(2 x), then sketch its graph.
- Find domain and range of p(x) = f(x) − x, then sketch its graph.

- For an application with differing units for input, it may be useful to begin with different names for the functions and their inputs. E.g., if distance D traveled in H hours is D = f(H) and same distance in M minutes is D = g(M), then look for a necessary relation between functions f and g as a consequence of the simple relation between H and M.
- The
**order of operations**can matter. For example, let a[x] = x − 3 and b(x) = 2^{x}, then compare f(x) = a[b(x)] with g(x) = b(a[x]).

- Let f be the function graphed in Figure 2.22 on page 89;
its domain is interval [0,4) and its range is set {1,2,3,4}.
- Work on these problems in section 6.3:
s3, s7, s9;
1, 9, 11,
**13**, 15, 17; 23, 25, 28–29, 41,**43**, 49, 53

- Study section 6.3
(
- We will prepare for chapters 7–9 by studying
*Right Triangle Ratios*, a chapter from a Trigonometry text added to the end of the UM Custom Edition on pages 561–617. Its four sections will be referred to as T.1–T.4. - Tuesday [d21]
WeBWorK:
RQ-T1-T2 closes at 10 am,
day-19 closes at 11 pm
- Study section T.1 (
*Angles, Degrees, and Arcs*) through Example 4 (Sun's Diameter). Two part–whole relations involving a central angle are important.- (central angle) : (360 degrees) = (arc length) : (circumference)
- (central angle) : (360 degrees) = (area of sector) : (area of circle)

- Work on these problems in section T.1:
1, 3;
39, 41, 43, 44;
51;
**58**, 61, 65 - Study section T.2 (
*Similar Triangles*). Section T.1 began with a discussion of*indirect measurement*; section T.2 applies that in the context of triangles with the "same shape". As you study its last example (**Explore/Discuss 2**), keep in mind that canyon depth y is to be computed in terms of direct measurements a, b, and c (computing x is optional). - Work on these problems in section T.2: 1, 5, 7; 11–12, 13, 15; 23, 25; 29, 33, 41
- Anticipate a quiz on Tuesday or Wednesday.

- Study section T.1 (
- Wednesday [d22]
WeBWorK:
RQ-T3-T4 closes at 10 am,
day-20 closes Thursday at 11 pm
- Study section T.3
(
*Trigonometric Ratios and Right Triangles*). Put a TI calculator into**Degree**mode to use it in sections T.3 and T.4. - Work on these problems in section T.3: 29, 30, 33, 37, 39, 41, 51; 59, 63, 65, 69
- Study section T.4 (
*Right Triangle Applications*). - Work on these problems in section T.4: 1, 3, 5, 13; 23, 27

- Study section T.3
(
- Friday [d23]
WeBWorK:
RQ-7-1 closes at 10 am,
day-21 closes Saturday at 11 pm
- Write-up solutions of these five problems —
show your work and interpret your results. Hand-in your written
homework at the
**start**of Friday's class.**section**6.3 T.1 T.2 T.3 T.4 **problems**38 70 34 64 14 - I suggest reviewing the
**Lighthouse Beacon**example on pages 250–251 while (or after) studying section 7.1. - Study section 7.1
(
*Introduction to Periodic Functions*). - Work on these problems in section 7.1:
2–5, 7, 9;
15, 19 & 21, 23,
30 (study discussion of figure 7.9 first),
**33**

- Write-up solutions of these five problems —
show your work and interpret your results. Hand-in your written
homework at the

© Richard B Lane
Last modified: 16 March 2017, Thursday 19:12