pc 1-1 notes -...
TRANSCRIPT
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1-‐1 Func+ons
*Describe subsets of real numbers. *Iden+fy and evaluate func+ons and
state their domains
Interval Nota+on Bounded Intervals Unbounded Intervals
Inequality Interval Nota+on Inequality Interval Nota+on
a ≤ x ≤ b [a, b] x ≥ a [a, ∞)
a < x < b (a, b) x ≤ a (-‐∞, a]
a ≤ x < b [a, b) x > a (a, ∞)
a < x ≤ b (a, b] x < a (-‐∞, a)
-‐∞ < x < ∞ (-‐∞, ∞)
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p. 9 (1-‐14) Write each set of numbers in set-‐builder and interval nota+on, if
possible. 2. x < -‐13 10. x ≤ 61 or x ≥ 67 6. -‐31 < x ≤ 64 14. x ≥ 32 8. x < 0 or x ≥ 100
Write x > 5 or x < –1 using interval nota9on.
A.
B.
C. (–1, 5)
D.
* A set of ordered pairs in which no two different pairs have the same x-‐value
A func9on is a special type of rela+on.
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p. 9 (15-‐28) Determine whether each rela+on represents y as a func+on of x 16. The input value x is the year and the output value y is the day of the week. 18. x y
.01 423
.04 449
.04 451
.07 466
.08 478
.09 482
20. x2 = y + 2
22. 4y2 + 18 = 96x
24. x = y – 6 y
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Determine whether 12x 2 + 4y = 8 represents y as a func9on of x.
A. Yes; there is exactly one y-‐value for each x-‐value.
B. No; there is more than one y-‐value for an x-‐value.
26. 28.
Func+on Nota+on
• f(x) is read “f of x” • The value of the func+on f at x
Equa+on: y = -‐6x Related Func+on: f(x) = -‐6x y = f(x)
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p. 9 (30-‐36) Find each func+on value.
30. g(x) = 2x2 + 18x – 14 a) g(9)
30. g(x) = 2x2 + 18x – 14
b. g(3x)
30. g(x) = 2x2 + 18x – 14
c. g( 1 + 5m)
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32. f(t) = 4t + 11 3t2 + 5t + 1
a) f(-‐6)
32. f(t) = 4t + 11 3t2 + 5t + 1
b) f(4t)
32. f(t) = 4t + 11 3t2 + 5t + 1
c) f(3 – 2a)
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34. h(x) = 16 -‐ 12 2x + 3
a) h(-‐3)
34. h(x) = 16 -‐ 12 2x + 3
b) h(6x)
34. h(x) = 16 -‐ 12 2x + 3
c) h(10 – 2c)
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36. g(m) = 3 + m2 − 4
a) g(-‐2)
36. g(m) = 3 + m2 − 4
b) g(3m)
36. g(m) = 3 + m2 − 4
c) g(4m – 2)
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If , find f (6).
A.
B.
C.
D.
find f (6)
Domain
• Set of all real numbers for which the expression used to define the func+on is real
• 2 main exclusions – Values that would result in division by zero – Values that would result by taking the even root of a nega+ve number
p. 10 (39-‐46) State the domain of each func+on in interval nota+on.
40. x + 1 x2 – 3x -‐ 40
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42. h(x) = 6− x2
44. g(x) = 3x2 −16
46. g(x) = 6 + 2 x + 3 x -‐ 4
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State the domain of g (x) = .
A. [4, ∞)
B. [–4, 4]
C. (− , −4]
D.
p. 10 (48-‐51) Find f(-‐5) and f(12) for each piecewise func+on.
48. f (x) =
−4x +3−x3
3x2 +1
if x < 3if3≤ x ≤ 8if x > 8
#
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Find f(-‐5) and f(12)
50. f (x) =
2x2 + 6x + 46− x2
14
ififif
x < −4−4 ≤ x <12x ≥12
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%&&
'&&
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ENERGY The cost of residen9al electricity use can be represented by the following piecewise func9on, where k is the number of kilowaZs. Find the cost of electricity for 950 kilowaZs.
A. $47.50
B. $48.00
C. $57.50
D. $76.50
Ticket out the door
Write your name, class period, the ques+on, and circled answer on a scrap sheet of paper. Be sure to turn it in for credit! Given evaluate f(3).
f (x) = −4xx2 −1
Homework
p. 8-‐12 # 1 – 7, 11, 15 – 37, 39 – 47, 49 – 53 odds # 80, 107-‐110 all