91Ó°ÊÓ

Granny Shots The last player in the NBA to use an underhand foul shot (a "granny" shot) was Hall of Fame forward Rick Barry, who retired in \(1980 .\) Barry believes that current \(\mathrm{NBA}\) 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 \(h(x)=-\frac{136 x^{2}}{v^{2}}+2.7 x+3.5,\) 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 initial velocity with which the ball must be shot 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 the height of the ball after it has traveled 9 feet in front of the foul line. (d) Find additional points and graph the path of the basketball.

Find the function that is finally graphed after each of the following transformations is applied to the graph of \(y=\sqrt{x}\) in the order stated. (1) Shift up 2 units (2) Reflect about the \(y\) -axis (3) Shift left 3 units

(a) Find the domain of each function. (b) Locate any intercepts. (c) Graph each function. (d) Based on the graph, find the range. $$f(x)=\left\\{\begin{array}{ll}x+3 & \text { if } x<-2 \\\\-2 x-3 & \text { if } x \geq-2\end{array}\right.$$

If (3,6) is a point on the graph of \(y=f(x),\) which of the following points must be on the graph of \(y=f(-x) ?\) (a) (6,3) (b) (6,-3) (c) (3,-6) (d) (-3,6)

Motion of a Golf Ball A golf ball is hit with an initial velocity of 130 feet per second at an inclination of \(45^{\circ}\) to the horizontal. In physics, it is established that the height \(h\) of the golf ball is given by the function $$ h(x)=\frac{-32 x^{2}}{130^{2}}+x $$ where \(x\) is the horizontal distance that the golf ball has traveled. (a) Determine the height of the golf ball after it has traveled 100 feet. (b) What is the height after it has traveled 300 feet? (c) What is \(h(500) ?\) Interpret this value. (d) How far was the golf ball hit? (e) Use a graphing utility to graph the function \(h=h(x)\). (f) Use a graphing utility to determine the distance that the ball has traveled when the height of the ball is 90 feet. (g) Create a TABLE with TblStart \(=0\) and \(\Delta \mathrm{Tbl}=25 .\) To the nearest 25 feet, how far does the ball travel before it reaches a maximum height? What is the maximum height? (h) Adjust the value of \(\Delta\) Tbl until you determine the distance, to within 1 foot, that the ball travels before it reaches its maximum height.

If (1,3) is a point on the graph of \(y=f(x),\) which of the following points must be on the graph of \(y=2 f(x) ?\) (a) \(\left(1, \frac{3}{2}\right)\) (b) (2,3) (c) (1,6) (d) \(\left(\frac{1}{2}, 3\right)\)

Based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Solve \(v=\frac{2.6 t}{d^{2}} \sqrt{\frac{E}{P}}\) for \(P\).

If (4,2) is a point on the graph of \(y=f(x),\) which of the following points must be on the graph of \(y=f(2 x) ?\) (a) (4,1) (b) (8,2) (c) (2,2) (d) (4,4)

Graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, \(y=x^{2}\) ) and show all the steps. Be sure to show at least three key points. Find the domain and the range of each function. $$ f(x)=x^{2}-1 $$

In Problems 37-48, determine algebraically whether each function is even, odd, or neither. \(f(x)=4 x^{3}\)