©Fry Texas A&M University
1. (2 points) !
a) −∞
2. (2 points) !
a) −∞
Math 150 Precalculus
f (x) = −x 2 (1− x 2 ) ! !
b) −1
c)
g(x) = −x 2 (1− x 3 ) !
b) −1
Spring 2014
As x → −∞ ,
0
f (x) →
d) 1
e) ∞
As x → −∞ , g(x) →
c)
0
d) 1
e) ∞
!
3. (2 points) !
a) −∞
4. (2 points) !
a) −∞
5. (2 points) !!
a) −∞
−x 2
h(x) =
(1− x 2 )
b) −1
p(x) =
−x 2
(1− x 3 )
b) −1
As x → −∞ ,
c)
0
!
As x → −∞ , p(x) →
c)
0
(1− x 3 )
r(x) =
−x 2
b) −1
h(x) →
d) 1
d) 1
e) ∞
e) ∞
As x → −∞ , r(x) →
c)
0
d) 1
e) ∞
3
©Fry Texas A&M University
Math 150 Precalculus
6. (8 points) Determine the x − intercept(s) of f (x) =
Spring 2014
4
1
1
+
. If there are none, write
x+2 x−3
NONE. Intercepts are points so, if there are any, state their x and y coordinates.
!
!
!
!
!
!
!
!
!
!
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x
1
≥
.Give your answer in interval notation.
x+2 x+2
7. (8 points) Solve
!
!
!
!
!
!
!
!
!
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©Fry Texas A&M University
Math 150 Precalculus
1− x − x + 4 = 1 ! !
8. (8 points) Solve
!
Spring 2014
5
________________________________
Solve 3 − x + 1 > 2 !. Give your answer in interval notation.
9. (8 points)!
!
!
!
!
!
!
!
!
!
!
!
!
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©Fry Texas A&M University
10. (13 points) If f (x) =
a)
2x + 5
3− x
b)
Math 150 Precalculus
3− x
.
2x + 5
2x + 5
x−3
Spring 2014
6
a) Then f −1 (x) =
!
5x − 3
2x + 1
c)
d)
3 − 5x
2x + 1
e) None of these
In interval notation state
b) the domain of f (x) ___________________
c) the range of f (x) _________________
d) the domain of f −1 (x) _________________!
e) the range of f −1 (x) _______________
11
!!
6+ 5
11. (5 points) Simplify
a)
6− 5
(
b) 11
6− 5
)
!
!
c) 11 11
!
d)
11
11
e) None of these
©Fry Texas A&M University
12. (5 points) Let g(x) =
a)
x2
(1− x )(1+ x )
b)
Math 150 Precalculus
1
1
and h(x) = .
x −1
x
2
x2
( x − 1)( x + 1)
Simplify ( g ! h ) ( x ) . ___________________
1
x ( x + 1) ( x − 1)
c)
Spring 2014
d) 1−
1
x2
e) None of these
x 2 + 3x + 2
. Determine the following. If there are none, write
x 2 − 2x − 3
NONE. State the intervals in interval notation. State the equation of lines. State both the x
and y coordinates of the points.
13. (8 points) Let f (x) =
a)
domain
________________!
b) y - intercept(s)
d) hole(s)
!
_____________! !
________________!
!
!
c)
x - intercept(s)
________________
e) vertical asymptote(s)
______________
7
©Fry Texas A&M University
Math 150 Precalculus
Spring 2014
14. (12 points) Simplify, if possible. Write UNDEFINED, if necessary.
a)
c)
e)
3
4
81 =
x7
____________
b)
= ____________
d)
18 + 8 =
____________
f)
5
4
128x18 =
____________
25 = ____________
1
3
5
= ____________
8
©Fry Texas A&M University
Math 150 Precalculus
Spring 2014
9
15. (8 points) Let f (x) = (x 2 + 1)(x − 2)2 Determine the following.
!
If there are none, write NONE. Intercepts are points so state their x and y coordinates.
a) y - intercept(s)
_____________! !
c) Solve (x 2 + 1)(x − 2)2 ≥ 0 !!
b) x - intercept(s)
________________
_____________________________________
d) Sketch the graph of f (x) = (x 2 + 1)(x − 2)2
(This sketch does not have to be perfect, but it should include the information you found above as well as
2
2
demonstrating the end behavior of f (x) = (x + 1)(x − 2) )
16. (7 points) Solve x 2 + x > 2 !
!
!
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