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Chapter 2: Q. 6 (page 68)
The set of all images of the elements in the domain of a function is called the _________.
The set of all images of the elements in the domain of a function is called the Blank.
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A wire meters long is to be cut into two pieces. One piece will be shaped as an equilateral triangle, and the other piece will be shaped as a circle.
Part (a): Express the total area Aenclosed by the pieces of wire as a function of the length x of a side of the equilateral triangle.
Part (b): What is the domain of A?
Part (c): Graph . For what value of xis Asmallest?
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 ?
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?
An equilateral triangle is inscribed in a circle
of radius r. See the figure. Express the circumference Cof the circle as a function of the length x of a side of the triangle.
[Hint: First show that .]
A wire of length xis bent into the shape of a circle.
Part (a): Express the circumference Cof the circle as a function of x.
Part (b): Express the areaAof the circle as a function ofx.
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