Math 1012 (Pre-calculus with recitation) MY9L Spring 2023 Instructor: Dr. Anthony E. Clement Test 1 (Sample) Name:- Part I: Do all 7 questions. Fill in the blanks. 1. The graph of x 2 + y 2 4x + 6y 12 = 0 is a circle with center ( , ) and radius . (6pts) 2. If a graph is symmetric with respect to the y-axis and (x, y) is on the graph, then ( , ) is also on the graph. (3pts) The graph of y = x 2+1 is symmetric with respect to the . (3pts) 3. The average rate of change of f(x) = x 2 + 1 on [5, 2] is-. On this interval y = x 2+1 is increasing/decreasing (circle one). (8pts) 4. The graph of y = f(x 5) is obtained from the graph of by shifting the graph of - horizontally - units -. (6pts) 5. Given the quadratic function f(x) = x 2 + 6x 8. a) f(x) has a local M- because(6pts) b) The local M of f(x) is: - (6pts) c) The vertex of f(x) is - (3pts) d) f(x) is increasing on the interval -(3pts) e) f(x) is decreasing on the interval -(3pts) 6. Let f(x) = 1 x1 and g(x) =1 x . a) (f g)(x) = - (3pts) b) (f g)(x) has domain:- (3pts) 7.(12pts) If 3x 5 3+20 = 76, then 3x 5 3= -. So x 5 3 = -. (x ) = . Let u = -. So u = -. u =- and u= = . Now x( )= . So x=- x =-, hence x = -. 2 Part II: Do this one question. Show all your work. 8. A small ball is thrown up in the air very softly by a boy 5 feet tall. The ball's height is given by h(x) = 3x 2 + 2x+ 5 , where x is the horizontal distance traveled by the ball from the boy's feet. a) (i) Find the maximum height attained by the ball and (ii) the horizontal distance traveled by the ball when it reached maximum b) Find the horizontal distance traveled by the ball when it hits the ground.(