Math 1050 Section 1 Review 1
Name:
Read all directions carefully. The review will be graded on completion and will be
worth 30 homework points. You can nd the complete solutions to the review posted
on my website www.math.utah.edu/~malone.
1. Simplify the expression
1024 7 2 5
16 3 3 4 2
100 2 + 4 4 100 5
w
x y
2. Completely factor 4
3. Find the domain of
7
x
x
z
x y
z w
x
x
p
( ) = ( p53) 3 4 +27
( + 7)
7 +1
x
f x
x
x
x
x
4. Find all real solutions to 7 2 10 2.
p
5. Find all real solutions to 5 + 1 7 = 9 and check that all solutions are
correct.
6. Find all solutions to the equation j + 5j j 4j = 15 and check that all your
solutions are correct.
7. Graph all the solutions to j4 8j 2 on the real number line.
8. Check algebraically whether the vertices (3 2) ( 1 4) and (5 1) form a right
triangle.
9. Plot the following 2 points (4 1) and ( 7 3) then nd the distance between
them and the midpoint on the line segment connecting them.
10. Write an equation for a circle with radius 7 and center ( 4 10).
11. Plot sucient points to sketch the graph of the equation j( 3)2 4j = .
12. Determine if the equation ( 2 +1) = 5 is symmetric with respect to the x-axis,
y-axis, or the origin.
13. Write an equation for the line passing through the points (2 11) and (15 7).
14. Write an equation for the line passing through the point (3 4) that is perpendicular to the line 4 + 7 10 = 0. In addition write an equation for the line
passing through the same point that is parallel to 5 9 = 14.
2
+ 5 3 2 then nd ( 2) (4) and (1) if they exist.
15. If ( ) =
2
j + 2j + 3
1
What is the domain of the function?
x
x
x
x
x
x
>
;
;
;
;
;
;
;
;
x
y
xy y
;
;
;
x
y
x
g x
x
x
x
x
x <
g
;g
y
;
g
16. If ( ) =
t x
x
3
2
x
+ 7 then nd and simplify the dierence quotient
(
) ( ) 6= 0
x
t x
h
t x
h
17.
18.
19.
;
h
.
Determine whether ( ) = 7 + 4 5 3 2 is even, odd, or neither.
Is ( 5)2 + ( + 1)2 = 16 a function? Why or why not?
Using your knowledge of transformations of functions and parent functions
sketch the graph of ( ) = x 1 7 + 5.
If ( ) = 3 7 and ( ) = j 2 7j + 1 then nd ( )( ), ( )( ), and
( )( ).
Determine weather or not ( ) = ( 9)3 + 2 has an inverse function or not.
If it does then nd the inverse function and show algebraically that it is an
inverse function.
Find the vertex, axis of symmetry, and x-intercepts for the quadradic function
( ) = 2 + 6 5.
Sketch the graph of ( ) = 7( 2)3 ( +4)2 by applying the leading coecient
test, nding the zeroes of the polynomial, and plotting sucient solution points
to draw a continuous curve through the points.
Perform the division
12 4 9 + 11 + 2
4 2 7
Find ( 2) when ( ) = 4 9 +9 8 3 7 +7 6 +36 5 +5 4 +10 3 2 2 +40 +153.
Simplify (4 3 )(3 + 7 ) (5 + 11)( 3 1) and write your answer in standard
form.
Find all real and complex solutions to 0 = 3 2 2 + 7 + 30
Find all the rational zeroes of 6 4 13 3 +48 2 91 +42. The way you should
proceed is as follows. Use Descartes's rule of signs to nd out how many are
possibly positive and how many are negative. Then use the rules for the upper
and lower bounds (try c=0 and c=2) to limit the options to choose from. This
is hard but try your best!!
State the domain of the rational function
2
6
( ) = 2 + 2 15
, identify all intercepts and asymptotes, then plot additional points as needed
to sketch the graph of the function.
Graph all solutions to 3 + 5 2 4 20 0 on the real number line.
Q x
x
x
x
x
y
P x
20.
f x
f =g
21.
22.
24.
g x
x
Y
f x
23.
x
f
f
x
g
f
x
x
x
x
x
x
M x
x
x
x
x
x
x
25.
26.
27.
28.
29.
f
f x
i
x
i
x
x
i
x
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x
x
x
x
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i
x
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L x
30.
x
x
x
x
x
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>
x
x
x
x