PreCalculus Accelerated
1.7 – More Practice
Name ______________________
Test Topics:
 Function Properties (What is a function? Even/Odd, One-to-one, Max/Min, Increasing/Decreasing)
 Function Operations and Composition
 Graphs and Transformations
 Inverses
 Word Problems and maximizing/minimizing
1) A rectangular package with square base to be sent by a postal service can have a maximum combined length
and girth (perimeter of a cross section) of 108 inches. Write the volume of the package as a function of x. Find
the dimensions of the box that maximize the volume. What is the maximum volume?
x
y
x
2) A rectangle is inscribed in a semicircle of radius 3. The equation of the semicircle is y  9  x 2 . Let P
(x,y) be a point in quadrant I that is a vertex of the rectangle and is on the circle. (See figure below).
a) Express the area of the rectangle as a function of x. For what value of x is the
area the largest? What is the largest possible area?
y  9  x2
b) Express the perimeter of the rectangle as a function of x. For what value of x
is the perimeter the largest? What is the largest possible Perimeter?
3) A 10 meter long wire is to be cut into two pieces. One piece will be shaped into an equilateral triangle, and
the other will be shaped into a circle. Let x be the length of the side of the equilateral triangle. Express the
total combined Area, A, as a function of x. For what value of x is the area the smallest? What is the smallest
Area?
4) Inscribe a right circular cylinder of height h and radius r in a sphere with radius 5. Express the volume of the
cylinder as a function of r. For what value of r is the volume the largest? What is the largest possible volume?
r
5
5) A right triangle has one vertex at the origin, another on the graph of y=9-x2 for x>0, and the third vertex on
the positive x axis at (x,0). See diagram below. Write the area of the triangle as a function of x. For what
value of x is the area of the triangle the largest? What is the largest possible area?
y=9-x2
(x,0)