Pre-Calc.
PRACTICE!
Chapter 1 Test
Name_____________________
Hour ________
Non-Calculator Part
1
1. Find the domain of
9  x2 .
Ans: 9 – x2 > 0
(3 – x)(3 + x) = 0
3 = x or -3 = x
-3
y  ( x  3) 5  2 x  3
-
+
2. Find f (x) and g (x) so that the function
y  f g (x) .
3
D: (-3, 3)
f ( x)  x 5  2 x
Ans: g ( x)  x  3
Graph the functions in problems 3, 4, and 5 using the transformation rules and the ten basic
functions. You must graph three points with your final graph!
3. f (x)  3 x  4
Start with (0, 0) (1, 1)
Vertical stretch of 3
(0, 0) (1, 3)
Right 4
(4, 0) (5, 3)
g x  
1
x3
2
5.
Start with
(-1, 1) (0, 0) (1, 1)
Reflect over x-axis
(-1, -1) (0, 0) (1, -1)
1
Vertical shrink of 2
1
1
(-1, 2 ) (0, 0) (1, 2 )
Left 3
1
2
4. h(x)  -( 2 x +3) -2
You need to factor
1
out the 2 inside the
function!
1
h(x)  -( 2 (x +6))2 -2
Start with
(-1, 1) (0, 0) (1, 1)
Reflection over (x-axis)
(-1, -1) (0, 0) (1, -1)
Horiz. Stretch of 2
(-2, -1) (0, 0) (2, -1)
Left 6
(-8, -1) (-6, 0) (-4, -1)
Down 2
(-8, -3) (-6, -2) (-4, -3)
2
6. If f ( x)  5x  2 and g ( x)  x  4 , find
 f  g (x) and state its domain.


Ans: f g x   5 x  4  2
 5x  4  2
 5x  20  2
 5x  22
D: [4, )
2
Pre-Calc.
PRACTICE!
Chapter 1 Test
Name_____________________
Hour ________
1
1
(-4, 2 ) (-3, 0) (-2, 2 )
7. Eliminate the parameter for the parametric
equations and simplify.
2
x  t and y  3t  2t .
Ans: x2 = t so y = 3(x2)2 – 2x2
y = 3x4 – 2x2
9. Find f 1 ( x) and its domain if
f ( x)  x  3  2 .
8. Describe the transformations of the graph of
f ( x)  2 x  2 into g ( x)  x  4  3
1
Ans: Vertical shrink of 2
Right 6
Up 3
Calculator Part
10. Is the function h( x)  x cos x even, odd, or
neither?
Ans: Find the domain and range of the original.
switch x and y, then solve for y. Switch the domain
and range for the inverse.
f ( x)  x  3  2
D : 3,  
Ans: h( x)   x cos( x)
  x cos(x)
Therefore it is an odd function. (You can also see
this from your calculator. I will not ask for an
algebraic verification on this problem.)
R : 0,  
x
y 3 2
x2
y 3
( x  2) 2  y  3
( x  2) 2  3  y
f 1 ( x)  ( x  2) 2  3
D : 0,  
11. Let
domain.
Ans:
f ( x) 
y
6x
x  4 . Find f
1
( x) and state its
6x
x  4 Switch x and y and resolve for y.
6y
y4
x( y  4)  6 y
x
xy  4 x  6 y
x 2  25
x2  9
Ans: The denominator cannot equal zero and the
radicand must be greater than or equal to zero.
12. Find the domain and range of y 
x2  9  0
( x  3)( x  3)  0
xy  6 y  4 x
x( y  6)  4 x
 4x
f 1 ( x) 
x6
x  3,3
x 2  25  0
x  5x  5  0
Pre-Calc.
PRACTICE!
Chapter 1 Test
Domain: (-  , 6) U (6,  )
Name_____________________
Hour ________
Plot the zeros and do the sign test.
+
-5
+
5
D :  ,5  5, 
Since 3 or -3 are not in these intervals, we do not
have to worry about them.
13. Determine whether the following function is
bounded above, bounded below, bounded, or not
bounded.
g x   2  x
14. A circle is inscribed in a square of side s.
Write the area of the circle as a function of s.
Ans:
2
s
Ans: bounded above
The area of a circle is A  r 2 . Since s  2r ,
s
then r  , and the area can be expressed as:
2
s
A   
2
s 2
A
4
x3
3
g ( x) 
4 x and
4x  1
15. Verify that
are inverses by showing f g ( x)  x and
f ( x) 
g  f ( x)   x
2
16. Find the endpoint of the parametric function if
t
y
2
0  t  4 and x  2t  5 and
t 3.
Ans: when t = 0 x = 2(0)2 – 5 = 0 – 5 = -5
0
0
 0
y = 03 3
when t = 4 x = 2(4)2 – 5 = 32 – 5 = 27
Pre-Calc.
PRACTICE!
Chapter 1 Test
3
 4x  1
3
 3

3
4x  1  4x  1 
4
x

1
f  g ( x)  

 3 
 3 
4
4


 4x  1 
 4x  1 
3  12 x  3
12 x
 4x  1 
x
12
12
4x  1
Name_____________________
Hour ________
4
4

y = 43 7
4
so the ordered pairs are (-5, 0) and (27, 7 ).
g  f ( x)  
3
3

 x  3
 x  3  4x
4
  1 4

 4x 
 4x  4x
3
3
3


 x
4 x  12  4 x 12 3
4x
4x x
17. State all extrema for the function
f x   x 3  3x  x  2 . Identify whether they
are local or absolute.
18. . Find all asymptotes of the function
3x
f ( x) 
4 x .
Ans: Graph and calculate any maximums or
minimums in your calculator.
Ans: horizontal asymptote: Compare the degree
of the numerator with the degree of the
denominator so
y = -3
vertical asymptote: Is where the denominator
equals zero so x =
Local max: (-0.92, 3.02)
Local min: (0.95, -0.28)
Since the domain is restricted to  2,  , there is a
minimum where x = -2. To find it use your table
to see what the point is.
Absolute min: (-2, -2)
19. State the intervals on which the function
x2
1  4 x 2 is increasing and decreasing.
Ans: Find vertical and horizontal asymptotes.
This will help with the intervals.
1
1
Increasing: [0, 2 ) U ( 2 ,  )
1
1
Decreasing: (-  , 2 ) U ( 2 , 0]
20. 4Is the following function continuous? If it is
discontinuous, state whether it is removable, jump,
or infinite discontinuity.
g x  
x
x
Ans: Discontinuous, jump
Pre-Calc.
PRACTICE!
Chapter 1 Test
21. The table to the right shows numbers of new
packaged goods products introduced to the
marketplace each year from 1986 to 1997.
a. Find a linear regression for the data using 1980
as year zero.
Ans:
In the STAT, EDIT menu, enter the data.
Then in the STAT, CALC menu, choose
linreg(ax+b)
On the home screen finish the expression
specifying Linreg(ax + b) L1, L2,Y1 and hit enter.
The equation y  1,164.05x  4,161.15 will
automatically be entered into your Y = menu.
b. Based on the regression line, approximately
how many new products would be introduced in
the year 2000?
Ans: Use 20 for x since it is 20 years after 1980.
The answer will be 27,442 products.
Name_____________________
Hour ________
Year
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
New Products
12,436
14,254
13,421
13,382
15,879
15,401
15,886
17,363
21,986
20,808
24,486
25,261