Berkeley City College Precalculus w/ Analytic Geometry - Math 2 - Chapters 1-3 Pt 2 Homework 2 Due: Name

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1 Berkele Cit College Precalculus w/ Analtic Geometr - Math 2 - Chapters 1-3 Pt 2 Homework 2 Due: Name Graph the function. 1) f() = + 1 if < 1-4 if 1 1) - - Objective: (2.4) Graph Piecewise-defined Functions Solve the problem. 2) An electric compan has the following rate schedule for electricit usage in single-famil residences: 2) Monthl service charge $4.93 Per kilowatt service charge 1st 300 kilowatts Over 300 kilowatts $0.1189/kW $ /kW What is the charge for using 300 kilowatts in one month? What is the charge for using 37 kilowatts in one month? Construct a function that gives the monthl charge C for kilowatts of electricit. Objective: (2.4) Graph Piecewise-defined Functions Instructor: K. Pernell 1

2 Match the correct function to the graph. 3) 3) - - A) = B) = - 1 C) = + 1 D) = - 1 Objective: (2.) Graph Functions Using Vertical and Horizontal Shifts Write the equation of a sine function that has the given characteristics. 4) The graph of = 2, shifted 6 units upward 4) Objective: (2.) Graph Functions Using Vertical and Horizontal Shifts ) The graph of =, shifted 9 units to the left ) Objective: (2.) Graph Functions Using Vertical and Horizontal Shifts 2

3 Graph the function b starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 6) f() = ( - 3)2-4 6) Objective: (2.) Graph Functions Using Vertical and Horizontal Shifts Write the equation that results in the desired transformation. 7) The graph of = 3, verticall compressed b a factor of 0.7 7) Objective: (2.) Graph Functions Using Compressions and Stretches Suppose the point (2, 4) is on the graph of = f(). Find a point on the graph of the given function. 8) = 4f() 8) Objective: (2.) Graph Functions Using Compressions and Stretches 3

4 Use the accompaning graph of = f() to sketch the graph of the indicated equation. 9) = - 2f( + ) + 4 = f() 9) Objective: (2.) Graph Functions Using Compressions and Stretches Match the correct function to the graph. ) 6 ) A) = B) = 1-2 C) = D) = -22 Objective: (2.) Graph Functions Using Reflections about the -Ais and the -Ais Find the function. 11) Find the function that is finall graphed after the following transformations are applied to the graph of =. The graph is shifted right 3 units, stretched b a factor of 3, shifted verticall down 2 units, and finall reflected across the -ais. Objective: (2.) Graph Functions Using Reflections about the -Ais and the -Ais 11) 4

5 12) Find the function that is finall graphed after the following transformations are applied to the graph of =. The graph is shifted up 2 units, reflected about the -ais, and finall shifted right 8 units. Objective: (2.) Graph Functions Using Reflections about the -Ais and the -Ais 12) Solve the problem. 13) Elissa wants to set up a rectangular dog run in her backard. She has 34 feet of fencing to work with and wants to use it all. If the dog run is to be feet long, epress the area of the dog run as a function of. Objective: (2.6) Build and Analze Functions 13) 14) A farmer has 00 ards of fencing to enclose a rectangular garden. Epress the area A of the rectangle as a function of the width of the rectangle. What is the domain of A? Objective: (2.6) Build and Analze Functions 14) 1) A farmerʹs silo is the shape of a clinder with a hemisphere as the roof. If the height of the silo is 78 feet and the radius of the hemisphere is r feet, epress the volume of the silo as a function of r. Objective: (2.6) Build and Analze Functions 1) 16) The volume V of a square-based pramid with base sides s and height h is V = 1 3 s 2h. If 16) the height is half of the length of a base side, epress the volume V as a function of s. Objective: (2.6) Build and Analze Functions

6 17) A bo with an open top is to be constructed from a rectangular piece of cardboard with dimensions inches b 20 inches b cutting out equal squares of side at each corner and then folding up the sides as in the figure. Epress the volume V of the bo as a function of. 17) 20 Objective: (2.6) Build and Analze Functions Use the slope and -intercept to graph the linear function. 18) f() = ) - - Objective: (3.1) Graph Linear Functions 6

7 Match the graph to one of the listed functions. 19) 19) A) f() = B) f() = C) f() = D) f() = Objective: (3.3) Graph a Quadratic Function Using Transformations 20) 40 20) A) f() = B) f() = 2-12 C) f() = D) f() = 2-12 Objective: (3.3) Graph a Quadratic Function Using Transformations Find the verte and ais of smmetr of the graph of the function. 21) f() = ) Objective: (3.3) Identif the Verte and Ais of Smmetr of a Quadratic Function 7

8 22) f() = ) Objective: (3.3) Identif the Verte and Ais of Smmetr of a Quadratic Function Determine the quadratic function whose graph is given. 23) 23) (0, 2) - (2, -2) - Objective: (3.3) Find a Quadratic Function Given Its Verte and One Other Point Determine, without graphing, whether the given quadratic function has a maimum value or a minimum value and then find that value. 24) f() = ) Objective: (3.3) Find the Maimum or Minimum Value of a Quadratic Function 2) f() = ) Objective: (3.3) Find the Maimum or Minimum Value of a Quadratic Function Solve the problem. 26) The manufacturer of a CD plaer has found that the revenue R (in dollars) is R(p) = -p2 + 1p, when the unit price is p dollars. If the manufacturer sets the price p to maimize revenue, what is the maimum revenue to the nearest whole dollar? Objective: (3.3) Find the Maimum or Minimum Value of a Quadratic Function 26) 8

9 27) You have 220 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maimize the enclosed area. Objective: (3.3) Find the Maimum or Minimum Value of a Quadratic Function 27) Use the figure to solve the inequalit. 28) f() < ) (-4, 0) (3, 0) Objective: (3.) Solve Inequalities Involving a Quadratic Function 29) 29) f() < g() Objective: (3.) Solve Inequalities Involving a Quadratic Function 9

10 30) 30) f() g() Objective: (3.) Solve Inequalities Involving a Quadratic Function Solve the inequalit. 31) ) Objective: (3.) Solve Inequalities Involving a Quadratic Function 32) > 0 32) Objective: (3.) Solve Inequalities Involving a Quadratic Function Solve the problem. 33) If f() = 62 - and g() = 2 + 3, solve for f() = g() 33) Objective: (3.) Solve Inequalities Involving a Quadratic Function 34) If f() = 62 - and g() = 2 + 3, solve f() g(). 34) Objective: (3.) Solve Inequalities Involving a Quadratic Function

11 Answer Ke Testname: 13SPR_CH1 3_MATH2_HW_2 1) - - 2) $39.70 $49.69 C() = 3) D 4) = ) = + 9 6) if if > ) = ) (2, 16) 9) ) C 11

12 Answer Ke Testname: 13SPR_CH1 3_MATH2_HW_2 11) = -( ) 12) = ) A() = ) A() = ; { 0 < < 00} 1) V(r) = π(78 - r)r πr 3 16) V(s) = 1 6 s 3 17) V() = ( - 2)(20-2) 18) ) A 20) A 21) (-, -2); = - 22) , ; = ) f() = ) minimum; ) maimum; ) $114,00 27) ft b ft 28) { -4 < < 3}; (-4, 3) 29) { < -1 or > 3}; (-, -1) or (3, ) 30) { -1 3}; [-1, 3] 31) [-1, ] 32) (-, -4) or (-2, ) 33) = 3 2, = ) - 1 3,