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Quiz #1 Review Unit 1. Properties of Functions
Quiz #1 Review
Unit 1. Properties of Functions
Suggested Problems 1
Find the domain and range for each of below functions.
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
Suggested Problems 2
Find the domain and range of each below functions.
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
Suggested Problems 1
Find the domain of each of function.
Suggested Problems 1 - SOLUTIONS -
Find the domain and range for each of below functions.
D: All real numbers D:
D: D:
D: D:
Suggested Problems 2
Find vertical and horizontal asymptotes of following functions. If no vertical or horizontal asymptotes, state no asymptotes.
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
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”
Trigonometric Identities
Use trig identities to prove following identities.
Suggested Problems 2
Text p.A32
Textbook p.A32 Prove the identity
45)
47)
49)
Suggested Problems 2 - SOLUTIONS -
Text p.A32
Textbook p.A32
45)
47)
49)
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.
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
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)
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
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)
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
Suggested Problems
Identify the transformations of each function from its parent function.
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.
