Math 131 Week in review 1 I Classify each function as a power function a polynomial a rational function or an exponential function and find f a for the given a a f x 5 3 a 2 c g x 6 3 x a 8 x b f x 4 x d h x e K x 18 x 24 x 32 5 a 2 3x 5 x 9x 4 2 a 1 a 2 3 II What are the domain and range of a function Find the domain and range of each function a f x x 2 b f x x 1 2 c f x x 1 2 WIR d g x x x 3x 4 2 1 A box will be made from a 50 inch by 20 inch cardboard by cutting equal size squares from the corners Describe the volume of the box as a function of the side of the square cutouts 2 Simplify the difference quotient f x h f x h 2 for f x x 3 x 3 A box has a rectangular base with length equal to twice the width The height of the box is 1 5 times the length Describe the volume as a function of the width f x 4 Find the domain of a 2 x 3x 2 b 1 g x 16 x 2 25 x 5 Graph the piecewise function f x 2 5 x 0 0 x 3x What is the domain of f Where is f increasing Where is f decreasing 6 Determine whether or not the points are collinear What is the least squares best fitting line Are any of the original points on the least squares line a 3 4 0 1 2 2 5 b 0 1 1 3 2 4 2 3 5 6 7 Factor each quadratic and find any roots or state no roots exist 2 a y x 3x 2 d y x 6 x 10 2 y 2x 3x 2 b 2 e c 2 y 9 x 12 x 5 2 y 16 x 8 x 1 8 Find the degree and leading term and leading coefficient of each polynomial a 7 24 x 4 x 3 b 8 5 x 7 x 90 9 For y 4 x 5 a if x increases by 1 unit then y b if x decreases by 2 units the y c if y increases by 3 units then x 10 A tree is 2 4 ft tall when planted It s height increases by 50 the first year and increases by 70 the second year a Describe the height of the tree using a piecewise linear model b Use quadratic regression to find a quadratic model What does the value of r 2 tell you in this case 11 An object is shot upward into the air with velocity v t 20 10 t cm sec where t is in seconds When is the velocity positive 0 negative When is the height increasing stationary decreasing 12 Each function is a transformation of a basic function Give the basic function and list the transformations in a proper order that result in the given function a f x 2 x 5 6 b f x 2 cos x 4 c f x x 2 x 6 d f x 15 x 2 x 2
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