1. Identifying Functions Group 2 questions 1.1 Is the following a function Choose One 3 points Yes No 1.2 Is the following a function? Choose One 3 points The Full Sail University catalog describes how letter grades and grade points are assigned based on the numerical grade in the class. A table showing Letter Grade, Numerical Grade, and Grade Points Is the relationship mapping a numerical grade to a letter grade a function? Yes No 2. Properties of Functions Group 5 questions 2.1 Is this function one-to-one? Choose One 3 points Let f:{a,b,c,d}{1,2,3,4} be given by f(a)=2 f(b)=1 f(c)=3 f(d)=4 Is this function one-to-one? Yes No 2.2 Is this function one-to-one? Choose One 3 points Let f:{a,b,c,d}{5,6,7,8} be given by f(a)=6 f(b)=6 f(c)=8 f(d)=7 Is this function one-to-one? Yes No 2.3 Is this function one-to-one AND onto? Choose One 3 points Let f:{a,b,c,d}{a,b,c,d} be given by f(a)=d f(b)=b f(c)=c f(d)=d Is this function onto? Yes No 2.4 Is this function onto? Choose One 3 points Let f:{1,2,3,4}{a,b,c,d} be given by f(1)=b f(2)=b f(3)=d f(4)=c Is this function onto? Yes No 2.5 Is this function onto? Choose One 3 points Let f:{a,b,c,d}{1,2,3,4} be given by f(a)=4 f(b)=2 f(c)=3 f(d)=1 Is this function onto? Yes No 3. Integer Functions Group 3 questions Functions in this section are integer valued. That means that input can only be integers and the output is an integer. Click here for a brief review of integers 3.1 Is this function one-to-one Choose One 3 points Let f:ZZ (a mapping from the set of integers to the set of integers) be given by f(n)=n2+1 Is this function one-to-one? Yes No 3.2 Is this function one-to-one? Choose One 3 points Is this function one-to-one? Yes No 3.3 Is this function onto? Choose One 3 points Is this function onto? Yes No 4. Real Valued Functions Group 3 questions Functions in this section are real valued. That means that input can be any real number, and the output can be any real number. Click here for a brief review of real numbers 4.1 Is this function one-to-one? Choose One 3 points Is this function one-to-one? Yes No 4.2 Is this function one-to-one? Choose One 3 points Is this function one-to-one? Yes No 4.3 Is this function onto? Choose One 3 points Is this function onto? Yes No 5. Floor and Ceiling Functions Group 7 questions 5.1 Compute: Choose One 3 points 4.3 4 5 5.2 Compute: Choose One 3 points 8.3+1 8 9 10 5.3 Compute: Choose One 3 points 6.7 -5 -6 -7 5.4 Compute: Choose One 3 points 10.2 10 11 5.5 Compute: Choose One 3 points 1.9 -1 -2 5.6 Compute: Choose One 4 points 10.2+8.7+2.2 20 21 22 23 5.7 Compute: Choose One 3 points 15.2+4 18 19 20 6. Domain, Target (Co-Domain), and Range Group 4 questions 6.1 What is the domain of the floor and ceiling functions? Choose One 3 points R : Set of Real Numbers Z : Set of Integers 6.2 What is the target (co-domain) of the floor and ceiling functions? Choose One 3 points R : Set of Real Numbers Z : Set of Integers 6.3 Identify the Range of a Function Choose One 3 points Is the range of the function toUpper(a):AA the same as the target? Reminder: The toUpper(a) function returns a capital version of any letter inputted. A = {a,A,b,B,c,C,d,D,e,E,...w,W,x,X,y,Y,z,Z } Yes: the Range = The Target No: the Range the Target 6.4 Identify the Range of a Function Choose One 3 points Is the range of the function f(x)=|x|:RR the same as the target? Reminder: The function f(x)=|x| is the absolute value of x Yes: The range = The target No: The range The target 6.4 Identify the Range of a Function Choose One 3 points Is the range of the function f(x)=| x|:RR the same as the target? Reminder: The function f(x)=|x| is the absolute value of x Yes: The range = The target No: The range The target 7. Identify Bijections Group 3 questions 7.1 Is the following function a Bijection Choose One 3 points Is a function that maps binary to natural numbers a bijection? A function is a Bijection when it is both onto and one-to-one. Yes No 7.2 Is the following function a Bijection? Choose One 3 points Is a function that maps usernames to accounts a bijection? A function is a Bijection when it is both onto and onetoone. Username refers to the login credentials, not other identifiers users/players use in a system/game o Yes o No 7.3 Is the following function a Bijection? Choose One 3 points Is a function that maps PlayerID (a number to unique to each player) to their GamerScore (points awarded in a game) a bijection? A function is a Bijection when it is both onto and one-toone. Yes No 8. Composition of Functions Group 2 questions 8.1 Calculate Choose One 3 points Given the following functions: f(x)=2x+9g(x)=x22 Identify the composition following composition of functions: (fg)(4) 17 37 287 8.2 Calculate Choose One 3 points Given the following functions: f(x)=2x+9g(x)=x22 Identify the composition following composition of functions: (gf)(4) 17 37 287 9. Function Inverse Group 2 questions 9.1 Identify the Inverse Choose One 3 points What is the inverse (f1) of the following function: f(x)=x2+3 f1=2x3 f1=2x6 The function is not invertible 9.2 Identify the Inverse Choose One 3 points What is the inverse (f1) of the following function: f(x)=3x+6 f1=13x6 f1=x32 The function is not invertible 10. Exponent Review Group 2 questions 10.1 Identify the equal expression Choose One 3 points Which of the following is equal to: axay axy ax+y axy axy 10.2 Identify the equal expression Choose One 3 points Which of the following is equal to: x5x3 x(53) x(53) 1x2 x8