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Practice Makes Perfect
In the following exercises, use the graph of the relation to:
- list the ordered pairs of the relation
- determine if the relation is a function
- find the domain of the relation
- find the range of the relation.
1.
- Answer
-
a. \((2, 3), (4, −3), (−2, −1), (−3, 4), (4, −1), (0, −3)\)
b. no
c. \({\{−3, −2, 0, 2, 4}\}\)
See Alsoma árabola d) straight line (−4,0) c) (0,−2) and (4,0) d) (0,2)... | Filo[PDF] 1) (-3) + (-6) = 2) (2) + (-5) = 3) (-7) + (-1) = 4) (-3) - (-6) = 5) (+2) - (+5) = 6) (-7) - (-4) = 7) (5)(-4) = 8) (-3)(-6) = 9) (-1)(2) = - Free Download PDFCA Foundation Question Paper with Solution June 2024d. \({\{−3, −1, 3, 4}\}\)
2.
3.
- Answer
-
a. \((1, 4), (1, −4), (−1, 4), (−1, −4), (0, 3), (0, −3)\)
b. no
c. \({\{−1, 0, 1}\}\)
d. \({\{−4, −3, 3,4}\}\)
4.
Determine if a Relation is a Function
In the following exercises, use the set of ordered pairs to:
- determine if the relation is a function
- find the domain of the relation
- find the range of the relation.
5. \( {\{(−3,9),(−2,4),(−1,1), (0,0),(1,1),(2,4),(3,9)}\}\)
- Answer
-
a. yes
b. \({\{−3, −2, −1, 0, 1, 2, 3}\}\)
c. \({\{9, 4, 1, 0}\}\)
6. \({\{(9,−3),(4,−2),(1,−1),(0,0),(1,1),(4,2),(9,3)}\}\)
7. \({\{(−3,27),(−2,8),(−1,1), (0,0),(1,1),(2,8),(3,27)}\}\)
- Answer
-
a. yes
b. \({\{−3, −2, −1, 0, 1, 2, 3}\}\)
c. \({\{0, 1, 8, 27}\}\)
8. \({\{(−3,−27),(−2,−8),(−1,−1), (0,0),(1,1),(2,8),(3,27)}\}\)
In the following exercises, use the mapping to:
- determine if the relation is a function
- find the domain of the relation
- find the range of the relation.
9.
- Answer
-
a. yes
b. \({\{−3, −2, −1, 0, 1, 2, 3}\}\)
c. \({\{0, 1, 2, 3}\}\)
10.
11.
- Answer
-
a. no
b. {Jenny, R and y, Dennis, Emily, Raul}
c. {RHernandez@state.edu, JKim@gmail.com, Raul@gmail.com, ESmith@state.edu, DBrown@aol.com, jenny@aol.cvom, Randy@gmail.com}
12.
In the following exercises, determine whether each equation is a function.
13.
a. \(2x+y=−3\)
b. \(y=x^2\)
c. \(x+y^2=−5\)
- Answer
-
a. yes
b. yes
c. no
14.
a. \(y=3x−5\)
b. \(y=x^3\)
c. \(2x+y^2=4\)
15.
a. \(y−3x^3=2\)
b. \(x+y^2=3\)
c. \(3x−2y=6\)
- Answer
-
a. yes
b. no
c. yes
16.
a. \(2x−4y=8\)
b. \(−4=x^2−y\)
c. \(y^2=−x+5\)
Find the Value of a Function
In the following exercises, evaluate the function: a. \(f(2)\) b. \(f(−1)\) c. \(f(a)\).
17. \(f(x)=5x−3\)
- Answer
-
a. \(f(2)=7\)
b. \(f(−1)=−8\)
c. \(f(a)=5a−3\)
18. \(f(x)=3x+4\)
19. \(f(x)=−4x+2\)
- Answer
-
a. \(f(2)=−6\)
b. \(f(−1)=6\)
c. \(f(a)=−4a+2\)
20. \(f(x)=−6x−3\)
In the following exercises, evaluate the function: a. \(g(h^2)\) b. \(g(x+2)\) c. \(g(x)+g(2)\).
21. \(g(x)=2x+1\)
- Answer
-
a. \(g(h^2)=2h^2+1\)
b. \(g(x+2)=4x+5\)
c. \(g(x)+g(2)=2x+6\)
22. \(g(x)=5x−8\)
23. \(g(x)=3−x\)
- Answer
-
a. \(g(h^2)=3−h^2\)
b. \(g(x+2)=1−x\)
c. \(g(x)+g(2)=4−x\)
24. \(g(x)=7−5x\)
In the following exercises, evaluate the function.
25. \(f(x)=3x^2−5x\); \(f(2)\)
- Answer
-
2
26. \(g(x)=4x^2−3x\); \(g(3)\)
27. \(f(x)=2x^2−3x+1\); \(f(−1)\)
- Answer
-
6
28. \(g(x)=3x^2−5x+2\); \(g(−2)\)
In the following exercises, solve.
29. The number of unwatched shows in Sylvia’s DVR is 85. This number grows by 20 unwatched shows per week. The function \(N(t)=85+20t\) represents the relation between the number of unwatched shows, N, and the time, t, measured in weeks.
a. Determine the independent and dependent variable.
b. Find \(N(4)\). Explain what this result means
- Answer
-
a. t IND; N DEP
b. \(N(4)=165\) the number of unwatched shows in Sylvia’s DVR at the fourth week.
30. Every day a new puzzle is downloaded into Ken’s account. Right now he has 43 puzzles in his account. The function \(N(t)=43+t\) represents the relation between the number of puzzles, N, and the time, t, measured in days.
a. Determine the independent and dependent variable.
b. Find \(N(30)\). Explain what this result means.
31. The daily cost to the printing company to print a book is modeled by the function \(C(x)=3.25x+1500\) where C is the total daily cost and x is the number of books printed.
a. Determine the independent and dependent variable.
b. Find \(N(0)\). Explain what this result means.
c. Find \(N(1000)\). Explain what this result means.
- Answer
-
a. x IND; C DEP
b. \(N(0)=1500\) the daily cost if no books are printed
c. \(N(1000)=4750\) the daily cost of printing 1000 books
32. The daily cost to the manufacturing company is modeled by the function \(C(x)=7.25x+2500\) where \(C(x)\) is the total daily cost and x is the number of items manufactured.
a. Determine the independent and dependent variable.
b. Find \(C(0)\). Explain what this result means.
c. Find \(C(1000)\). Explain what this result means.
