"MATH 107 QUIZ 2Instr: Instructions:? The quiz is worth 74 points.There are 6 problems.Your score on the quiz will beconverted to a percentage and posted in your Portfolio with comments.? This quiz is open book and open notes, and you may take as long as you like on itprovided that you submit the quiz no later than the due date posted in our course scheduleof the syllabus.You may refer to your textbook, notes, and online classroom materials,but you may not consult anyone or any online resource.? You must show all of your work to receive full credit.If you do not show work, youmay earn only partial or no credit.? Please type your work in your copy of the quiz, or if you prefer, create a documentcontaining your work.Scanned work is also acceptable.Be sure to include your name inthe document.Review instructions for submitting your quiz in the Quizzes and ExamsConference.? If you have any questions, please contact me by e-mail.At the end of your quiz you must sign the following dated statement with your name typed inlieu of a signature.Without this signed statement you will receive a zero. I have completed this quizmyself, working independently and not consulting anyone except theinstructor.I have neither given nor received help on this quiz.Name: Date: ? NAME: _______________________________ Math 107Quiz 274pts 1. (8 pts) For each of the graphs below state if the graph is the graph of a Function.Also foreach graph state if the graph is symmetric with respect to the x-axis, y-axis or the origin.If thegraph is not symmetric to x-axis, y-axis or the origin, write None.(no explanation required.) (There may be more than one graph which represents a function or possesses symmetry.)(A) (B) (C)(D) A. Function: Yes/No B. Function: Yes/No Symmetry: ____the x-axis_____ Symmetry: _____None_________C. Function: Yes/No D. Function: Yes/No Symmetry: _____No_________ Symmetry: ______y-axis________2. Consider the points 2, 7 and 5 2, ? 7? ? ? ?(a. 5 pts.) State the midpoint of the line segment with the given endpoints.if you have to coordinates (a,b) and (c,d) the mid point (x,y) of the line connecting the two pointsis given by;2 + 5 2? = = 3 227- 7 ? = = 02 So the mid point is (? ? ,0) (b. 5 pts.) Find the distance between the points. Show some work. Give the exact answer (involving aradical),simplify the radical as much as possible. 2 2 D= 5 2- 2 + - 7- 7 = 2 153. (2 pts. each) Consider the following graph of y = f (x). (Some of the points are plotted with using dots, foryour convenience.) (no explanations required) (a) State the y-intercept(s).The graph crosses the y-axis at 5, sothe yinterceptis (0, 5)(b) State the value of f(-2).When x = –2, the corresponding y- value is -3,sof ( –2) = -3. (c) State the domain in interval notation.{x | –2=x =3 } = [ – 2, 3] Domain: set ofinputs, x-values of the points on thegraph. (d) State the range in interval notation.{y | –3=y =6 } = [ – 3, 6] Range: set ofoutputs, y-values of the points on thegraph.23 x ? 4. (3 pts. each) Givenfx () ?x ? 5(a) Calculate f (10)2* 10- 3 ? 10 = = 1.133310 + 5(b) State the domain of the function. Express your answer in interval notation.23 x ? fx () ? has domain {x| x??-5}, or in interval notation,( -8, -5)?(-5,8)x ? 5 (c) Find the coordinates of the x-intercept(s).substitute 0 for y0 2? - 3 3 = = ? 2? - 3? ? =1 ? + 5 2 (3/2, 0) (d) Find the coordinate of the y-intercept.substitute 0 for x2* 0- 3 3 ? (0) = =-0 + 5 5 (0,-3/5) (e) Find and simplify as much as possible: f (t ?1) .2* ? + 1 - 3 2? - 1 ? ? + 1 = = ? + 1 + 5 ? + 6 5. (3 pts each)Given: f (x)?? 2x 4 (a) Calculate f (10)? 10 = 2* 10- 4 = 4 (b) State the domain of the function.Express your answer in interval notation.2x -4 =0 ?2x= 4 ? x = 2Domain (2, 8) (c) Find the coordinates of the x-intercept(s).Put y=0(2,0) (d) Find the coordinates of the y-intercept. Put x=0(0 , 2i)2 ?? t ? 4(e) Find and simplify as much as possible: f . ?? 2 ?? 2 2 ? + 4 ? + 4 ?= 2- 4 2 2 2 6.(3 pts each)Given f (x) ? x ?3and g(x) ? 2x ?1, find each of the following:a.fg ? )(5 ? ? 2 2? +? =? - 3 + 2? + 1 =? + 2? - 22? +?5 = 5 + 2* 5- 2 = 33b.fg)(x? ? 2? ? = (? - 3)(2? + 1)c.g ?f)(x ? ? 2 2 2? -?? = 2? + 1- ? - 3 = 2? + 1-? + 3 = 2? -? + 2 ?? f d.? 2? ? ?? g ?? 2 ? ? - 3 ? =? 2? + 1 2- 2 - 3? 5 + 10 2- 2 = =? 7 2*- 2 + 1 13 Bonus:In Calculus the difference quotient,is the calculation used to find thef (x?? h) f (x) h 2 f (x) ? 3x average rate of change of a function.Find the difference quotient for: .Simplify youranswer.(5 pts) 2 2 2 2 2? ? +? -? (? ) 3 ? +? - 3? 3? + 3? + 6? ? - 3? = =? ? ? 2 3? + 6? ? = 3? + 6?? At the end of your quiz you must sign the following dated statement with your name typedin lieu of a signature.Without this signed statement you will receive a zero. I have completed this quizmyself, working independently and not consulting anyone except theinstructor.I have neither given nor received help on this quiz.Name: Date:"