Activity 8 - Exam 2 Review Sheet Please put all work on a separate piece of paper! Show all work in order to receive credit. Do not use a calculator on problems #1-13 1. Assume ( 1, 3) is on the graph of f(:n). If 12(3) = 2f(:c), what point must be included in Mm)? E'l)(1.6) b)(2,5) c=)(1s3) d)(-%.3) 9)(2.3) 2. Assume (1, 3) is on the graph of f(:c). If f(;z:) is an odd function, what additional point must be included in f(:1:)? a) ( 1,3) b) (1,3) c) (1, 3) d) ( 3, 1) e) (3, 1) 3. Multiply and simplify the complex number: ( 2i "()2 a) 45282' b) 45+28i c) 9 d) 53 4. Simplify 3'57 a) 1' b) 1' c)1 d) 1 5. What is the vertex of the parabola f(;z:) = (:1: + 3)2 5 ? a) (3,5) b) (3, 5) c) (3, 5) d) (3,5) 256+? ifm 3 m+5 m3 Find the domain and range too. Graph the function: f($) = { Use your graphing calculator to find the intervals of increase and decrease for the function zz) = $4 23:3 113:1 + 5. Show your graph and window dimensions. Round all values to the nearest thousandth. Given u?) = 35.22 + 2a." - - - - - r h f $ Find a Simplified expressmn for $1 A farmer has 8500 meters of fencing and wants to enclose a rectangular plot that borders a river. What is the largest area that can be enclosed if fencing is needed along the river? L_-._',_ ._-.._.-_- _:.-._-.._;_ (a) Find a function that models the area of the enclosed plot in terms of a: where 5.2 represents the length of one side of the plot shown in the picture. (b) What is the value of m that will maximize total area? Justify! (c) What is the maximum area? 17. Find all four solutions (including any complex solutions) of the polynomial equation: 1:4 + 132:2 48 = 0 18. Find all solutions (including any complex solutions) to the quadratic equation: 19. 20. 21. 22. 23. 24. 3x24:c=7 If f(:z:) = 2:1:2 4:1: 3 and g(:t:) = a: 3. Find (f og)(a:) and simplify it completely. Divide: \"I\"? 1'. Find ( 2')?\" Given f(:1:) = 3:1:2 + 12:1: + 11, find: a) Vertex b) x-intercept(s) (Must be EXACT value(s), not approximation(s)) c) y-intercept(s) d) Domain Range e) Graph Given f(a:) = 33:2 + 6x 2, find: a) Vertex b) xintercept(s) (Must be EXACT value(s), not approximation(s)) c) y-intercept(s) d) Domain Range e) Graph A box without a top is to be constructed from a square piece of sheet metal 18 inches on each side cutting equal squares of size :1: from each corner and then folding up the sides. (a) Write a function for the volume V of the box in terms of :1: and find the domain of the function. (b) Use a graphing calculator to find the largest volume that the box could have AND the length of the corner cut, 2:, that would give the largest volume. 25. 26. A man wishes to put a fence around a rectangular field and then subdivide the eld into 4 smaller rectangular plots by placing three fences parallel to one of the sides. If he can only afford 2000 yards of fencing, what dimensions will give the maximum rectangular area? A farmer with 2000 meters of fencing wants to enclose a rectangular plot that borders on a straight highway. If the farmer does not fence the side along the highway, what is the largest area that can be enclosed