Name MATH 1111 College Algebra Homework 2 As it is always the case that correct

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Name MATH 1111 College Algebra Homework 2 As it is always the case that correct answers without sufficient mathematical justification may not receive full credit, make sure that you show all your work. Please circle, draw a box around, highlight, or otherwise clearly indicate your final answer for each question. By signing your name above, you attest to the fact that the work you are presenting is wholly your own. Attach all work to this coversheet. 1) Use the graph of the function f.given to the right, to answer the following questions Is f decreasing on the interval (-4,2)? b) a) Is f increasing on the interval (5,6)? c) List any intervals on which f is decreasing. d) Does the graph of f contain a local maximum? A local minimum? If so, list the ordered pair(s) for the extrema. (-2,1) 2) Plot the point (4,-2). Then, plot the point that is (4,0) symmetric to it with respect to a) the x-axis, b) the y-axis, and c) the origin. (0,0) (6,0) 3) Algebraically, i.e. without plotting points or looking at the graph, determine if the graphs of following equations exhibit any type of symmetry. List all types of symmetry, if any, that are present. List whether each function is even, odd, or neither a) y=x"-2x2-8 2x The last player in the NBA to use an underhand foul shot was Hall of Fame forward Rick Barry, who retired in 1980. Barry believes that current NBA players could increase their free-throw percentage if they were to use an underhand shot. Since underhand shots are released from a lower position, the angle of the shot must be increased. If a player shoots an underhand foul shot, releasing the ball at a 70-degree angle from a position 3.5-feet above the floor, then the path of the ball can be modeled by the function h(x) =--+ 2.7x + 3.5, where h is the height of the ball above the floor, x is the forward distance of the ball in front of the foul line, and v is the initial velocity with which the ball is shot in feet per second. a) The center of the hoop is 10 feet above the floor and 15 feet in front of the foul line. Determine the 4) 136x2 initial velocity with which the ball must be shot in order for the ball to go through the hoop. b) Write the function for the path of the ball using the velocity found in part (a). c) Determine h(9). What does this value represent? 5) Find the average rate of change of the function f(x)-x+1 a) from 0 to 2. b) from 1 to 3. c) from-1 to 1 if -2sx

Explanation / Answer

1.

a) yes the function is decreasing on the given interval because the slope of the function in negative in the interval

b) No , the function is decreasing in interval (5,6) as slope is negative in the given interval

c ) intervals are : ( -4,2 ) and (5,6)

d ) Local Maxima at x = 5 and y = 3

i.e ( 5, 3 )

Local Minima at x = 2 and y = -2

i.e ( 2 , -2 )

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