Functions and word problems practice.
Round all answers to the hundredth. You will need a graphing calculator.
Name: ______________________
1) An open box with a square base has a volume of 50 cubic inches.
a) If the square base has length x, write a function for the surface area, A(x), of the box in terms of x.
b) Find the length of x that would minimize the surface area and state the minimum surface area.
2) A rectangle has one vertex on the origin, one vertex on the positive x –axis, one vertex on the positive y-axis, and one
vertex on the graph at the point P (x,y). (As shown in the diagram)
a) Write an equation that models the perimeter as a function of x.
P(x,y)
b) Find the maximum perimeter of the rectangle.
c) Write an equation that models the area as a function of x.
d) Find the maximum area of the rectangle.
e) Find an equation for the distance from the point (x,y) to the point (3,0)
as a function of x.
 1
3

3) Graph f  x    x  2
 x  1  1

if    x  2


if  2  x  5

4) Find the domain of h ( x ) given that h  x   3  x  4 .
x
odd, even or neither? Justify algebraically.
x2  1
Remember, format matters. Look in your notes if you’ve forgotten.
5) Is f ( x) 
6) If g ( x ) 
x3
find the RANGE of g 1 ( x )
x6
7) Use the functions below to find each of the following: (Write domains in interval notation)
f  x 
2x
x 3
g  x  x  5
h  x 
3x
x2
k ( x)  4  x
a) g  f  4    _______
b) f k and its domain _____________________________
 f  h1 =______
d) h  x   f  x  and its domain _______________________
c)
e) h h and its domain _________________________ f)   and its domain _____________________________
h
f
g) g  k and its domain ________________________
h) g 1 ( x )
__________________________
Domain of g ( x ) _______
Range of g ( x )
_______
Domain of g 1 ( x ) ______
Range of g 1 ( x) _______
Make a quick sketch of both functions.
8)
y
a) Write a piecewise function from the graph.
4
f(x)
4
x
b) Find all increasing intervals.
c) Find the x values where f ( x )  0
d) Find all values of x such that f ( x)  1