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Relations and Functions – Class WorkName _________________________________Is the relation a function?1,2, 3,4, 5,64,3, 3,2, 4,25,1, 3,1, -4,1 28892595253016259525304800952529845069853016256985304800698533159701250950041845312559000 415925133985414235178700 Relations and Functions – Home WorkIs the relation a function?3,1, -2,6, 1,41,2, 2,2, 1,22,1, 5,1, -6,72984509525301625952530480095252889259525302895952537592088902841371226900 3727451206500376555-127000331524957900Spiral ReviewSimplify each of the followingx4-3?2x42x2y4?4x2y4?3x3x-3y22x3z23x3y4z2?x-4z3Evaluating Functions – Class WorkName _________________________________Find the following:If fx= 3x+4, Find f2If fx=-x-3, Find f(19) If If hx= x-4, Find h-6If gx=3x3, Find g-2If fx=2x2-2, Find f2-aIf hx=x-22+2, Find h(2b+1)If gx=2x2-x, Find gm-2If fx=12x + 3, Find f(4x2)Evaluating Functions – Home WorkFind the following:If fx= x-12, Find f-5If fx=-2x-3, Find f(-4) If If hx= x3-1, Find h-2If gx=-2x2-1, Find g4If fx=-3x +2, Find f-x-6If hx=2x-12, Find h(1-2p)If gx=x3-x, Find ga2If fx=8x2 , Find f(2m)Spiral ReviewMultiply each of the following(4x+1)(2x+6)(7x-6)(5x+6)(x2+6x-4)(2x-4)Interval and Inequality Notation – Class WorkName _________________________________Give the interval and inequality notation for each graph.35242554610 33337525400 31432576835 352425-106045 35242560960 352425-87630 30480092710 2266952032000 14351011811000 1847855842000 Interval and Inequality Notation – HomeworkGive the interval and inequality notation for each graph.29527548260 29527548895 35242569215 29527557150 31432558420 29527549530 29527560325 2266956667500 23431512827000 2679704826000 Spiral ReviewSimplify each of the following(x-2?x-3)46x2y23x-1?4yx22pm-1q0-42m-1p32pq2Discrete vs. Continuous – Class WorkName _________________________________Is the relation discrete or continuous? If continuous, state the interval of continuity.1,2, 3,4, 5,64,3, 3,2, 4,2 5,1, 3,1, -4,13079758890301625889030480088902984506985301625698530480069853048006985312420698530480003028959525Discrete vs. Continuous – Home WorkIs the relation discrete or continuous? If continuous, state the interval of continuity.3,1, -2,6, 1,41,2, 2,2, 1,2{(2,1), (5,1), (-6,7)}2984509525301625952530480095252984509525292100698530480095253028959525302895952530289503028959525Domain and Range – Class WorkName _________________________________4349115-1905Find the domain and range for each of the following. Write your answers in interval notation where appropriate.1,2,3,4,5,64,3,3,2,4,22423795977902317758890451485762044015191193370029400541328003333752286000 For some functions below, you may need to use a graphing calculator or on an online program(like ) to find the range. fx=-23x-3gx=2-x hx=12x-5 gx=-x-2 fx=(x-2)3+1 hx=x2Domain and Range – Home WorkFind the domain and range for each of the following. Write your answers in interval notation where appropriate.3,1, -2,6, 1,41,2, 2,2, 1,23930651079540894012065350520127004400551079543132863786400304725274400445135294900 For some functions below, you may need to use a graphing calculator or on an online program(like ) to find the range. hx=-23x2gx=-2x-1 fx=13x-2 hx=3x2-x+2 fx=2x-35 gx=-2x3x+4Operations with FunctionsName _________________________________Class WorkGiven: and Given that fx=3x2-4, gx= 3x-2-1, and hx=fx+gx.Find: a) h(x)b) h(2) c) h(0) d) the domain of h(x)Given that fx=2x-3, gx=-3x2, and hx=fxgx.Find: a) h(x)b) h(-2) c) h(1) d) the domain of h(x)Given that fx=x-3, gx=-2x2, and hx=fxgx.Find: a) h(x)b) h(2a) c) h(m - 2) d) the domain of h(x)Given that fx=2-x, gx=3x-2, and hx=2fx-3gx.Find: a) h(x)b) h(-4p) c) h(1 - k) d) the domain of h(x)Given that fx=3x+1, gx=x-2 hx= f(x)(g(x))2Find: a) h(x)b) h(2a) c) h(1 - p) d) the domain of h(x)Operations with FunctionsHomework Given fx=x+5, gx=2x+12 and hx=fx-gxFind: a) h(x)b) h(4) c) h(-5) d) the domain of h(x) Given fx=2-x, gx=4-x and hx=g(x)fxFind: a) h(x)b) h(2) c) h(0) d) the domain of h(x)Given fx=x-5, gx=x+2 and hx=gxfxFind: a) h(x)b) h(30) c) h(3k - 2) d) the domain of h(x)Given fx=-2x3-1, gx=2x2-x and hx=5fx-2gxFind: a) h(x)b) h(a2) c) h(- m) d) the domain of h(x)Given fx=2x-3, gx=2-3x, and hx= -f(x)(g(x))2Find: a) h(x)b) h(1 - x) c) h(2b) d) the domain of h(x)Spiral Review123. Graph:124. Graph:125. Factor:126. Multiply: y=-x-3+5 y=-x+2-4 16x2 – 81 (2x + 3)(4x2 + 2)Composite FunctionsName _________________________________Class Work fx=3x-2; gx=-2x+4Find:a) g°fb) (g°f)(-3) fx=x2+1; gx=5x-1Find:a) f(g(x)) b) f(g(0)). fx=2x-2; gx=2x2-9Find:a) f°gb) (f°g)(6) fx=xx2-1+3; gx=x+2Find:a) f(g(x)) b) f(g(-2)). fx=x3; gx=x-1Find:a) g°fb) (g°f)(-2) Composite FunctionsHomework fx=-12x+3; gx=-4x+2Find:a) g°fb) (g°f)(2) fx=2x2-5; gx=2x+3Find:a) f(g(x)) b) f(g(-1)) fx=-1x+2; gx=3x2-10Find:a) f(g(x)) b) f(g(0)) fx=xx2+4+3; gx=2-xFind:a) f(g(x)) b) f(g(-3)) fx=x2-4; gx=x-1Find:a) g°fb) (g°f)(3)Spiral Review137. Graph:138. Graph:139. Simplify:140. Multiply: y=-log?(x+3) y=2x+22-4 -5x3y-325x-7y-2 (-2m2n3)(-8m5n4)Inverse FunctionsName _________________________________Class Work (2 pages) fx=3x-2i) Given f(x), find f-1(x) ii) Algebraically show that f(f-1(x)) = f-1(f(x)) = x. 36893509144000iii) Graph f(x) and f-1(x) on the same graph. iv) Describe the domain and range for f -1(x). fx=2x2+1 *domain is restricted to [0,∞) i) Given f(x), find f-1(x) ii) Algebraically show that f(f-1(x)) = f-1(f(x)) = x. 37731706667500iii) Graph f(x) and f-1(x) on the same graph. iv) Describe the domain and range for f -1(x). fx= 31-x2 *domain is restricted to [0,∞) i) Given f(x), find f-1(x) ii) Algebraically show that f(f-1(x)) = f-1(f(x)) = x. 36893501968500iii) Graph f(x) and f-1(x) on the same graph. iv) Describe the domain and range for f -1(x). fx=34x-2i) Given f(x), find f-1(x) ii) Algebraically show that f(f-1(x)) = f-1(f(x)) = x. 37946324826000iii) Graph f(x) and f-1(x) on the same graph. iv) Describe the domain and range for f -1(x).Spiral Review145. Find: f ? g146. Factor:147. Simplify148. Graph:If g(x) = x2 + 2 16x2 –25y2 (-2x3y2)4 y=-3x+2and f(x) = (x – 1)2Inverse FunctionsHomework (2 pages) fx=5x+2i) Given f(x), find f-1(x) ii) Algebraically show that f(f-1(x)) = f-1(f(x)) = x. 36893509144000iii) Graph f(x) and f-1(x) on the same graph. iv) Describe the domain and range for f -1(x). fx=23x2-6 *domain is restricted to [0, ∞) i) Given f(x), find f-1(x) ii) Algebraically show that f(f-1(x)) = f-1(f(x)) = x. 37731706667500iii) Graph f(x) and f-1(x) on the same graph. iv) Describe the domain and range for f -1(x). fx= x-4i) Given f(x), find f-1(x) ii) Algebraically show that f(f-1(x)) = f-1(f(x)) = x. 365760012890500iii) Graph f(x) and f-1(x) on the same graph. iv) Describe the domain and range for f -1(x). fx=-3x+2i) Given f(x), find f-1(x) ii) Algebraically show that f(f-1(x)) = f-1(f(x)) = x. 37946324826000iii) Graph f(x) and f-1(x) on the same graph. iv) Describe the domain and range for f -1(x).Unit ReviewMultiple Choice – Determine the best answer for each question.Determine the domain of 1,3, 5,6, 6,81, 5, 81, 5, 6 3, 6, 8Set of RealsDetermine the range of fx=x-2+3.3, ∞1, ∞1, ∞(3, ∞)3000375108585What is the domain of the graph to the right?-10≤x≤10-10<x<10-6≤x≤-2 or 0≤x≤-6-10≤x≤-4 or -2≤x≤4 or 6≤x≤10Which choice represents a discrete set?The time it takes people to tie their shoes.The amount of rain in a given week.The number of people attending a play.The number of rotations of a wheel.Which of the following is a function?x2+y2=4x+y2=4x2+y=44x2+y2=4 fx=3x2-2 , gx=4-x, and hx=fx-gx. h(3) =78262418 fx=3x2-2 , gx=4-2x, and hx=fx/gx. h(3) =-50-2525-12.5 fx=(3x)2-4 , gx=5-4x, and hx=fxgx. h(3) =-539-161-77 fx=3x2-2 , gx=4-x, and hx=f(gx). h(3) =-5-3-11 fx=3x2-2 , gx=4-x, and hx=g(f(x)). h(2a + 1) =-12a2-12a+325-36a+12a2-6a2+512a2+3 Given fx=2x3-2, find f-18-102235122 Given fx=2x3-2 and f-1a=-3, find a.-27-33-56undefinedShort Constructed Response13) Evaluate the function at all of the given points. y=2x-9+3a) f(25)b) f(9)c) f(10)d) f(3x – 4)14) Find f + g, f – g, fg and f/g for the following functions. Then, find their domain.fx=x-1, g(x) = 3x2 + 215) Evaluate the function for f(x) = x2 – 1 and g(x) = x + 2a) (f + g)(2)b) (f – g)(-1)c) (fg)(3)d) (f/g)(0)16) Find f ? g and g ? f:a) f(x) = x2, g(x) = x + 3b) f(x) = 2x – 5, g(x) = x2 + 217) Determine whether the function has an inverse function. If it does, find the inverse function.a) f(x) = 3x2*domain restricted to [0, ∞)b) fx=3x+1 c) f(x) = 1/xd) f(x) = 2x + 3Extended Response fx=(x-2)3+4i) Given f(x), find f-1(x) ii) Algebraically show that f(f-1(x)) = f-1(f(x)) = x. 37731702476500iii) Using technology to help you, graph f(x) and f-1(x) on the same graph. iv) Describe the domain and range for f -1(x).Relations and FunctionsClassworkFunctionNot a FunctionFunctionFunctionFunctionNot a FunctionNot a FunctionNot a FunctionFunctionFunctionFunctionFunctionNot a FunctionRelations and FunctionHomeworkFunctionFunctionFunctionFunctionNot a FunctionNot a FunctionFunctionNot a FunctionNot a FunctionFunctionNot a FunctionFunctionFunction Evaluating FunctionsClass Workf2=10f19=-4h-6=10g-2=-24f2-a=2a2-8a+6h2b+1=4b2-4b+3gm-2=2m2-9m+10 f4x2=18x2+3Evaluating FunctionsClass Workf(-5)=36f-4=-11h-2=-9g4=-33f-x-6=3x+20h1-2p=16p2-8p+1ga2=a6-a2f2m=2m28x2+26x+635x2+12x-362x3+8x2-32x+16Interval and Inequality NotationClasswork1, ∞x≥1-∞, -3x<-3-2, 6-2≤x≤6-3, 1-3≤x<11, 91<x<9-∞, 0x≤0[0, ∞)x≥0-8, -4 or [2,∞)-8≤x≤-4 or x≥2-∞, -7 or -5, ∞x≤ -7 or x>-5-∞, -5 or 4, ∞x ≤-5 or x>4Interval and Inequality NotationHomework-4, ∞x≥-4-∞, 2x<2-5, 3-5≤x≤32, 62≤x<6-8, 0-8<x<0-∞, 5x≤5-9, ∞x≥-9-4, 0 or (5, ∞)-4≤x≤0 or x>5-∞, -4 or 2, ∞x< -4 or x>2-6, 0 or (3, ∞)-6<x≤0 or x>3Spiral Review1x202xy16x6y5z2Discrete vs. ContinuousClassworkDiscreteDiscreteDiscreteDiscreteDiscreteDiscreteDiscreteDiscreteDiscreteDiscreteContinuous-4, ∞Continuous-∞, -2 or 2, ∞ContinuousAll Real NumbersDiscrete vs. ContinuousHomeworkDiscreteDiscreteDiscreteDiscreteDiscreteDiscreteDiscreteDiscreteDiscreteDiscreteContinuous[-6, 6]Continuous-8, 0ContinuousAll Real NumbersDomain And RangeClassworkD:1, 3, 5R:2, 4, 6D:3,4R:2, 3D:-4, 0, 2R:3, 4, 5D:4, 5, 6R:6D:-2, -1, 2, 3R:0, 3, 4, 5, 7D: 1, 2R:3, 4, 5, 6D:x≤-2 or x>2R:All Real NumbersD:All Real NumbersR:y≥2D:All Real NumbersR:All Real NumbersD:All Real NumbersR:All Real NumbersD: x ≤2R: y ≥0D: x>52R: 2.24>y>0 (approximately)D: All Real Numbers R: y≤0D: All Real Numbers R: All Real Numbers D: All Real Numbers R: y ≥0Domain And RangeClassworkD:-2, 1, 3R:1, 4, 6D: 1, 2R:2D:-1, 0, 1R:6, 7, 8D:2, 4R:6, 7, 8D:3, 4, 5, 6R:1, 2, 3, 4D:5R:0, 1, 2, 3D:-4, -2, 2, 4, 5R:-3, 2, 4, 5D: -6≤x≤6R: -6≤y≤6D: x ≥-2 R:All Real NumbersD:x≠0R:y<0(4x-9)(4x+9)8x3+12x2+4x+6a) -6x+8 b) 26128. a) 25x2-10x+2 b) 2129. a) 22x2-11 b) 261130. a) x+2x+1 b) 0131. a) x3-1 b) 9132. a) 2x - 10 b) 10133. a) 8x2+24x+13 b) -3134. a) -13x2-8 b) 18135. a) 2-x6-x+3 b) 59+3136. a) x2-5 b) 4137. 138. 139. -x105y140. 16m7n7i) f-1x=x+23ii) ff-1x=3x+23-2=x+2-2=xf-1fx=3x-2+23=3x3=xiii) iv) The domain and range are both the set of all real numbers.i) f-1x=x-12ii) ff-1x=2x-122+1=2x-12+1=x-1+1=xf-1fx=2x2+1-12=2x22=xiii) iv) D:x≥1, R: y≥0i) f-1x=1-x3ii) ff-1x=31-1-x32=31-1-x3=3x3=xf-1fx=1-31-x23=1-1-x2=x2=xiii) , dashed line is f-1, dotted line is f. iv) D:x ≤1, R: y ≥0i) f-1x=34x+12ii) ff-1x=3434x+12-2=33x+2-2=33x=xf-1fx=3434x-2+12=3124x-2+12=34x-212+12=12x-6+612=xiii) , dashed line is f. iv) D:x≠0, R: y≠12f°g=x4+2x2+1(4x-5y)(4x+5y)16x12y8i) f-1=x-25ii) ff-1x=5x-25+2=x-2+2=xf-1fx=5x+2-25=xiii) iv) D:-∞,∞, R:(-∞,∞)i) f-1x=32x+9ii) ff-1x=2332x+92-6=2332x+9-6=x+6-6=xf-1fx=3223x2-6+9=x2-9+9=x2=xiii) iv) D: x≥6, R:y≥0i) f-1x=x2+4ii) ff-1x=x2+4-4=x2=xf-1fx=x-42+4=x-4+4=xiii) iv) D:x≥0, R: y≥4i) f-1x=-x+23ii) ff-1x=-3-x+23+2=x-2+2=xf-1fx=-(-3x+2)+23=3x-2+23=3x3=xiii) iv) D:-∞,∞, R:(-∞,∞)Unit Review:badcccda9abca) 11, b) 3, c) 5, d) 23x-4+3f+g=3x2+x+1, D: (-∞,∞)f-g=-3x2+x-3, D: (-∞,∞)fg=3x3-3x2+2x-1, D: (-∞,∞)fg=x-13x2+2, D:(-∞,∞)a) 7, b) -1, c) 40, d) -1/2a) f°g=x2+6x+9, g°f=x2+3b) f°g=2x2-1, g°f=4x2-2x+27a) yes, f-1x=x3b) yes, f-1x=x3-1c) yes, f-1x=1xd) yes, f-1x=x-32i) f-1x=3x-4+2ii) ff-1x=3x-4+2-23+4=3x-43+4=x-4+4=xf-1fx=3x-23+4-4+2=3x-23+2=x-2+2=xiii) iv) D:-∞,∞, R: (-∞,∞) ................
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