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Chapter 2: Q. 9 (page 89)
Concepts and Vocabulary
True or False: A function f is decreasing on an open interval I if, for any choice of x1 and x2 in I, with x1 < x2 , we have
True
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Use the given graph of the function f to answer parts (a) 鈥� (n).
(a) Find and .
(b) Find and .
(c) Is positive or negative?
(d) Is positive or negative?
(e) For what values of x is ?
(f) For what values of x is localid="1650172833683" ?
(g) What is the domain of f ?
(h) What is the range of f ?
(i) What are the x-intercepts?
(j) What is the y-intercept?
(k) How often does the line y = -1 intersect the graph?
(l) How often does the line x = 1 intersect the graph?
(m) For what value of x does ?
(n) For what value of x does ?
The following sketch represents the distance d (in miles) that Kevin was from home as a function of time t (in hours). Answer the questions based on the graph. In parts (a) 鈥� (g), how many hours elapsed and how far was Kevin from home during this time?
(h) What is the farthest distance that Kevin was from home?
(i) How many times did Kevin return home?
According to physicist Peter Brancazio, the key to a successful foul shot in basketball lies in the
arc of the shot. Brancazio determined the optimal angle of the arc from the free-throw line to be 45 degrees. The arc also depends on the velocity with which the ball is shot. If a player shoots a foul shot, releasing the ball at a 45-degree angle from a position 6 feet above the floor, then the path of
the ball can be modeled by the function
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. Suppose a player shoots a ball with an initial velocity of 28 feet per second.
(a) Determine the height of the ball after it has traveled 8 feet in front of the foul line.
(b) Determine h(12). What does this value represent?
(c) Find additional points and graph the path of the basketball.
(d) The center of the hoop is 10 feet above the floor and 15 feet in front of the foul line. Will the ball go through the hoop? Why or why not? If not, with what initial velocity must the ball be shot in order for the ball to go through the hoop?
True or False The domain and the range of the reciprocal function are the set of all real numbers.
Medicine Concentration: The concentration C of a medication in the bloodstream t hours after being administered is modeled by the function .
(a) After how many hours will the concentration be highest?
(b) A woman nursing a child must wait until the concentration is below before she can feed him. After taking the medication, how long must she wait before feeding her child?
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