Chapter One Test Review
NAME: ___________________
Read all directions carefully. Be sure to show work and if you use your calculator, write down what you
punched in or what the graph on the calculator looks like (be sure to label points).
1) Test for all four symmetries.
You must show work on your test or give an explanation to receive credit!
x3 + y3 = 4 Only y = x symmetry
2) Find the domain of the following. Be sure to use interval notation!
x5
7 x
a) f  x  
b) f  x   4  x
c) f  x   x 2  9
d) f  x  
3 x
x 5
 ,3  3,  
   3  3,  
 5,  
 4,  
3) Describe each transformation below.
a.
b.
c.
d.
e.
f.
g.
y = -f(x)
y – b = f(x)
y = 3f(x)
y = f(-x)
y = f(x + 3)
x = f(y)
y = f(1/2x)
reflected across x-axis
shifted up
vertical stretch (pulled toward y-axis, thinner)
reflected across y-axis
shifted left 3
inverse
horizontal stretch (pulled toward x-axis, wider)
4) Using a calculator, graph k ( x)  x 4  5x 2  4 .
Adjust your viewing window to 4  x  4, 5  y  5 .
Use your calculator to help you find the find the following values.
Round to the nearest hundredth and use interval notation!
a) Domain  ,   and Range  2.25,  
b) Zeros  2,0  &  1,0 
c) y-intercept of k  0, 4 
d) Maximums  0, 4  and Minimums  1.59, 2.25
e) Intervals of Increasing  1.59,0  & 1.59,   and Decreasing  , 1.59  &  0,1.59 
f) Is k a function? Explain how you know. Yes, passes the VLT
g) Does k have an inverse function? Explain how you know. No, fails the HLT
5) Given f  x   2 x  3 and g  x   x  4 , find a)  f 1 g 1   x 
b)  g 1 f   2 
x7
2
5
x2
are inverses.
3
Each order of composition, f(g(x)) and g(f(x)) should simplify to ‘x’
6) Use composition of functions to varify that f  x   3x  2 and g  x  
7) If x varies directly as y when x = 20 and y = 5, find
a) the value of k
k = 1/4
x
4
c) use the equation you wrote to find x when y = 12
b) a model, using k, to relate x and y y 
y = 48
8) Write a model to represent that area of a triangle varies jointly as one half the base
1
times the height. A  bh
2
9) Write a model to represent: M varies inversely with P and Q and directly with the square
root of r and t.
( x  2)2
10) Given f  x   
 x3
M
k  rt 
kt r
or M 
PQ
PQ
if
x0
if
x0
, sketch a graph of the function.
 x 2  2, x  2

11) Given f  x   5, -2  x  0 , sketch a graph of the function.
8 x  5, x  0

12) The numbers of foreign students, F (in thousands) enrolled in colleges in the United
States from 1992 to 2002 can be approximated by the model.
F  0.004t 4  0.46t 2  431.6, 2  t  12
Where t represents the year, with t=2 corresponding to 1992.
a) Sketch a graph of the function.
On your calculator, in your window settings, make xmin = 2 and xmax = 12
Then do a zoom fit
b) Find the average rate of change from 1992 to 2002.
= 14.728
13) Find the average rate of change between f  0  and f  3 when f  x   3x 2  x  2 .
= 10
14) Also try the following problems:
Pgs 106 – 108, #’s 11-22 all, 28, 43-50 all, 57-68 all, 74,
75-84 all (parts a-c only), 85-88 all & 91-94 all.
(problems 46, 49, 62, 65 & 74 are similar to WebAssign)
Look in back of book for odd problem answers and/or go to www.calcchat.com for
odd problem solutions.