12th TRIVIA QUIZ SPORTS QUIZ (first thematic quiz) Claudy Rayan.
Quiz #1 Review - cdsapcalcab2014.weebly.com€¦ · Quiz #1 Review Unit 1. Properties of Functions...
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Quiz #1 Review
Unit 1. Properties of Functions
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Suggested Problems 1
Find the domain and range for each of below functions.
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Suggested Problems 1 - SOLUTIONS -
Find the domain and range for each of below functions.
D: All real numbers
R: All real numbers
D: All real numbers
R: All real numbers
D: All real numbers
R:
D: All real numbers
R: y = 0
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Suggested Problems 2
Find the domain and range of each below functions.
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Suggested Problems 2 - SOLUTIONS -
Find the domain and range of each below functions.
D: All real numbers
R: All real numbers
D: All real numbers
R: …because its vertex is and the graph faces upward.
D: All real numbers
R: …because its vertex is and the graph faces upward.
D: All real numbers
R: All real numbers
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Suggested Problems 1
Find the domain of each of function.
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Suggested Problems 1 - SOLUTIONS -
Find the domain and range for each of below functions.
D: All real numbers D:
D: D:
D: D:
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Suggested Problems 2
Find vertical and horizontal asymptotes of following functions. If no vertical or horizontal asymptotes, state no asymptotes.
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Suggested Problems 2 - SOLUTIONS -
Find vertical and horizontal asymptotes of following functions. If no vertical or horizontal asymptotes, state no asymptotes.
H.A.: None V.A.: x = 1
H.A.: y = 5 V.A.: x = 2, -2
H.A.: y = 2 V.A.: None
H.A.: y = 0 V.A.: x = -1
H.A.: y = 0 V.A.: x = -1
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Suggested Problems 1 - SOLUTIONS -
Now with more respect for graphs of beautiful trig functions, sketch following six trig functions.
All graphs are shown on the lesson slides of “03. Trigonometric Functions”
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Trigonometric Identities
Use trig identities to prove following identities.
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Suggested Problems 2
Text p.A32
Textbook p.A32 Prove the identity
45)
47)
49)
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Suggested Problems 2 - SOLUTIONS -
Text p.A32
Textbook p.A32
45)
47)
49)
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Suggested Problems
Fill in the below table of values for the function, , and then plot the points.
x -2 -1 0 1 2
f(x)
Find domain and range.
If possible, find x-intercepts and y-intercept.
Find any asymptotes.
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Suggested Problems - SOLUTIONS -
Fill in the below table of values for the function, , and then plot the points.
x -2 -1 0 1 2
f(x) -1/8 -1/4 -1/2 1 -2
Find domain and range.
D: All real numbers
R: y < 0
If possible, find x-intercepts and y-intercept.
No x-intercepts
y-intercept at (0, -1/2)
Find any asymptotes.
H.A. at y = 0
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Suggested Problems 1
Fill in the below table of values for the logarithmic function , and then identify followings.
Domain: Range: x-intercept (if exist): y-intercept (if exist): End-Behavior: Asymptotes (if exist):
x ¼ ½ 1 2 4
f(x)
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Suggested Problems 1 - SOLUTIONS -
Fill in the below table of values for the logarithmic function , and then identify followings.
Domain: x >0 Range: All real numbers x-intercept (if exist): (1, 0) y-intercept (if exist): None End-Behavior: As As Asymptotes (if exist): V.A. at
x ¼ ½ 1 2 4
f(x) 2 1 0 -1 -2
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Suggested Problems 2
Fill in the below table of values for the logarithmic function , and then identify followings.
Domain: Range: x-intercept (if exist): y-intercept (if exist): End-Behavior: Asymptotes (if exist):
x ¼ ½ 1 2 4
f(x)
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Suggested Problems 2 - SOLUTIONS -
Fill in the below table of values for the logarithmic function , and then identify followings.
Domain: x > 0 Range: All real numbers x-intercept (if exist): (1/4, 0) y-intercept (if exist): None End-Behavior: As As Asymptotes (if exist):
x ¼ ½ 1 2 4
f(x) 0 1 2 3 4
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Suggested Problems
Identify the transformations of each function from its parent function.
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Suggested Problems
Identify the transformations of each function from its parent function.
Shift right 3, and shift up 4 Shift 2 left, and reflect about x-axis
Stretch vertically by factor of 4, reflect about x-axis, and then shift up 5
Stretch horizontally by factor of 1/3, and reflect about y-axis
Shift left by 4, stretch horizontally by factor of 1/3, stretch vertically by factor of 2, and then shift up 5.
Shift right 3, stretch vertically by factor of 2, and then shift up 4.