PreCalculus Assignments– Fall 2017

Essential question: What precalculus concepts are necessary for success in AP Calculus?

Day / Topic / Assignment
Mon
July 31 / EQ: How can we write the equation of functions that are made from known graphs?
- Go over syllabus and expectations
-Writing the equation of lines and piecewise
-transformations of known graphs
-even and odd functions / Read syllabus, Turn in prereq packet for completion Piecewise Functions , transformations
Prereq Packet #24-26, 35,45-53, 101,102, 105, 107, 108, 109, 111-114
BoAS (baottom of assignment sheet) #1 & 2
p.19 #3, 4, 11, 25, 51-56, 69, 71-75, 77, 78
Tues
Aug 1 / EQ: How do I determine the domain of functions? How do I transform e and ln graphs?
-Domain
-transformations of e & ln graphs / Quick Homework Quiz
Domain and Range ; e-ln transformation handouts
Ticket out the door
Prereq Packet #29-34, 104, 126
p. 21 #31-38,42,43 p. 42 #1, 4-7,9,11,13,21, 27
Wed
Aug 2 / EQ: What trigonometry do I need to know?
- common trig values
-All Students Take Calculus
-Solving Trig Equations -ArcTrig Functions / Quick Homework Quiz
Known Trig Values, Arctrig and Solving Arctrig
Prereq packet #83-90 BoAS #3, 4
p. 71 #63-72
Thurs
Aug 3 / EQ: How do I simplify exponential and logarithmic functions? How do I solve exponential and logarithmic equations? How can I evaluate function values from a chart and a graph?
- New functions from old
- Exponential Fcts - Logarithmic Fcts / Mid-Unit Quiz on Precalculus concepts
Functions with a chart and graph, e/ln Review
Prereq Packet #36-44, 67-77,116-118,120,135-137
BoAS #5
p. 43 #29, 31, 50, 51
p. 57 #1-3
p. 70 #21-23,25
Fri
Aug4 / EQ: How do I solve inequalities? How do I find inverses?
- solving rational inequalities
-discussion on solving inequalities
-absolute value -inverse functions / Quick Homework Quiz
Inequality HandoutAbsolute Value
Prereq packet #14-21, 132-134
Ticket out the door
p. 50 #21-23
Mon 8/7 / review / Old Test as review
Tues 8/8 / Test on PreCalculus / Turn in Prereq packet for accuracy grade!

BoAS#1: 1. Given the graph of the rational function , algebraically

a. find the x-int b.find the y-int c. find the eq of the horizontal asym. d. find the eq of the vertical asym.

# 2. Does ? Explain.

#3. Given , the equation of a circle, find an expression for

a. the bottom half the circle b. the right half the circle. c. the bottom left quarter of the circle.

#4. Write a function that expresses the following-

a. the radius of a circle in terms its circumference. b. the area of a circle in terms of its circumference.

c. the diagonal of a square in terms of its side.d. the area of a square in terms of its diagonal.

e. the surface area of a cube in terms of its volume.

#5. a. Use a graphing calculator to determine that has only one solution.

b. Use a graphing calculator to determine that has 3 solutions and find their value to 3 decimal places.

c. Find an approximate value of m such that the equation has exactly two solutions.

Answers to homework problems: p. 19 #3 (a) f(1)=3, (b) f(-1) ≈ −0.2 (c) f(x) = 1 is equivalent to y = 1. When y = 1,

x = 0 and x = 3. (d) y = 0 when x ≈ −0.8 (e)d: [ −2, 4] r: [−1, 3] (f) [−2, 1] #4 (a) f(─4) = ─2, g(3) = 4 (b) x = 2, ─2

(c) x = ─3, 4 (d) [0, 4] (e) domain: [-4, 4] range: [-2, 3] (f) domain [-4, 3] range [0.5, 4]

#11 The person’s weight increased to about 160 lbs at age 20 and stayed fairly steady for 10 years. Then the person’s weight dropped to about 120 lbs for the next 5 years, then increased rapidly to about 170 lbs. The next 30 years saw a gradual increase to 190 lbs. Possible reasons for the drop in weight at 30 years of age: diet, exercise, health problems. #25 f(2) =12 f(-2) = 16 f(a) = f(-a) = f(a+1)=

2f(a)= f(2a)= #51

#52 f(x) = -5/3 x + 5/3, -5 ≤ x ≤ 7 #53 #54

#55 #56

#69 f is odd bc symmetric about origin, g is even bc symmetric wrt y-axis #71 (a) (-5, 3) (b) (-5, -3)

#72 a) reflect y –axis b) rotate 180° about origin #73 odd #74 even #75neither

#77 even#78 neither BoAS #1 (a) (b) (c) y = 2 (d) x = 7 #2 no! order of oper.

Day 2 P. 21 #31x ≠ -3, 3 #32 x ≠ -3, 2 #33 #34 -2 ≤ t ≤ 3 #35 x < 0 ᴗ x > 5#36 u ≠ ─2, ─1 #37 [ 0, 4]#38 domain [-2, 2] range [0, 2]#42 graph the line f(t) = t + 2, but put a hole in the graph at the point (2, 4)#43 g is the top half of the parabola with vertex at (5, 0) turning right p. 42 #1 (a) y = f(x)+3 (b) y=f(x) – 3 (c) y=f(x - 3) (d) y = f(x+3) (e) y = − f(x)

(f) y = f(−x) (g) y = 3f(x) (h) y = f(x) #4a) points on new graph (-2, -3) (1, 0) (2, 0) (3, -1) #4b) (0, -1) (3, 2) (3,3) (5, 1)

#4c) (-2, 2) (-1, 0)(0, -2) (1, -4) (2, -4)(3, -2) #4d) (-6, 0) (3, 3) (6, 3) (9, 2) #5 (a) shrink horizontally by ½ (b) stretch horizontally by2 (c) reflect about y-axis (d) reflect about y-axis and then about x-axis

#6 #7 y = -1 f(x+4)−1 to reflect x-axis, shift 4 units to left and then down 1. So#9 start with y = 1/x and then shift 2 left #11 start with and then reflect x-axis

#13 start with y = and then shift 2 to right and 1 down. #21 start with and then shift 2 right #27 (a) graph the portion of y = f(x) to the right of the y-axis and then reflect about y-axis. (b) (c)

Day 3 p. 71 #63 (a) (b) π #64 (a)(b) #65 (a) (b) #66 (a)(b) #67 (a) 10 (b) #68 a) (b) #69 Let y = . Then . Therefore, cosy≥0 so

#70 #71 #72 BoAS #3 a) (b) (c) part a answer with dom x≥1

BoAS #4 a) (b) (c) (d) (e) Day 4 p. 43 #29 (a) d:

(b) d: (c) d: (d)

#31 (a) (b) (c) (d) 4x+3 d: #50) (a) 5( b)2 (c) 4 (d) 3 (e) 1 (f) 4 #51 (a) 4 (b) 3 (c) 0 (d) und (e) 4 (f) −2 p. 57 #1 (a) 4 (b) #2(a) 16 (b) #3 (a) (b) 648y

p. 70 #21 #22#23 #25

BoAS#5 (a) 0.739 (b) -3.294, -2.356, 1.202 (c)

Day 5 p. 50 #21 -0.72 and 1.22#22 1.29 #23 0.65 #25 g(x) is greater than f(x) whenever x > 100