Math 1330 Final
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1) Find the x- and y-intercepts of the following function.
f ( x )  =  x 2 − 8 x + 15
a) x-intercept: ( 15 , 0 ) ; y-intercept:
*b) x-intercepts: ( 5 , 0 ) and ( 3 , 0 ) ;
c) x-intercepts: ( 5 , 0 ) and ( − 3 , 0 ) ;
d) There are no x- or y-intercepts.
e) x-intercepts: ( − 5 , 0 ) and ( 3 , 0 ) ;
f) None of the above.
( 0 , − 15 )
y-intercept: ( 0 , 15 )
y-intercept: ( 0 , 15 )
y-intercept: ( 0 , 15 )
2) Give the vertical asymptote(s) for the graph of
*a)  x = 7
b) x = 10 , x = − 7
c) x = 7 , x = − 10
d) x = − 7
e) x = 4 , x = 7
f) None of the above.
3) Find the inverse of the given function, if possible.
f ( x )  =  x 2 + 3 , where x ≥ 0
 − 1 ( x )
a) f
 =  √ x  − 3
− 1
b) f    ( x )  =  − √ x  + 3
c) f  − 1 ( x )  =  √ x + 3 
d) f ( x ) does not have an inverse.
*e) f  − 1 ( x )  =  √ x − 3 
f) None of the above.
4) Which of the following functions could represent the graph given below?
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a)
b)
c)
d)
*e)
f) None of the above.
5) Which of the following functions would result in the graph shown below?
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a) f ( x )  =  ( x + 1 )5 − 2
b) f ( x )  =  − ( x + 1 )5 + 2
c) f ( x )  =  − ( x − 1 )4 − 2
d) f ( x )  =  ( x − 1 )5 + 2
*e) f ( x )  =  − ( x − 1 )5 + 2
f) None of the above.
6) Complete the square to write the equation in the standard form, f ( x )  =  a ( x − h )2 + k.
f ( x )  =  2 x 2 + 28 x + 96
7 )2
+ 47
a) f ( x )  =  2 ( x +
2
b) f ( x )  =  2 ( x + 7 ) + 2
*c) f ( x )  =  2 ( x + 7 )2 − 2
d) f ( x )  =  2 ( x − 7 )2 + 47
e) f ( x )  =  2 ( x − 14 )2 − 2
f) None of the above.
7) Write the equation of the circle whose diameter has endpoints ( 8 , 8 ) and ( 4 , 12 ).
a) ( x − 6 ) 2  +  ( y − 10 ) 2  =  2 √ 2 
b) ( x + 6 ) 2  +  ( y + 10 ) 2  =  2 √ 2 
c) ( x + 6 ) 2  +  ( y + 10 ) 2  =  8
d) ( x + 6 ) 2  +  ( y + 10 ) 2  =  32
*e) ( x − 6 ) 2  +  ( y − 10 ) 2  =  8
f) None of the above.
8) State the length of the minor axis and the coordinates of the vertices of the minor axis for the given ellipse.
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a) Length of minor axis: 2; Coordinates of vertices: ( − 3 , 0 ) ( 3 , 0 )
*b) Length of minor axis: 4; Coordinates of vertices: ( 0 , − 2 ) ( 0 , 2 )
c) Length of minor axis: 3; Coordinates of vertices: ( 0 , − 2 ) ( 0 , 2 )
d) Length of minor axis: 5; Coordinates of vertices: ( − 3 , − 2 ) ( 3 , 2 )
e) Length of minor axis: 6; Coordinates of vertices: ( − 3 , 0 ) ( 3 , 0 )
f) None of the above.
9) Find the  x-coordinate(s) of the point(s) of intersection for the following functions below:
f ( x )  =  x 2 + 2 x − 1
g ( x )  =  2 x  +  3
a) {0, − 4}
b) {− 2, 2}
c) {1, 2}
*d) {2, − 2}
e) {4, − 4}
f) None of the above.
10) Find the vertex of the quadratic function
f ( x )  =  9 x 2 − 90 x + 3
a) ( 9 , − 28 )
b) ( 5 , 228 )
c) ( − 5 , − 222 )
d) ( 5 , − 84 )
*e) ( 5 , − 222 )
f) None of the above.
11) Which of the following is equivalent to sin 2 (θ)  −  sec 2 (θ) + cos 2 (θ) + tan 2 (θ) ?
a) csc 2 (θ)
b) − 1
c) cot (θ)
d) 1
*e) 0
f) None of the above.
12) Which of the following is equivalent to
sin (θ) + cos (θ)
2
− 2 sin (θ) cos (θ) ?
*a) 1
b) 0
c) sin 2 (θ)  −  cos 2 (θ)
d) 2
e) 1 − 2 sin (θ) cos (θ)
f) None of the above.
13) Evaluate: sin 
4π⁄
3
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a) √ 3 
b) − 1⁄2
*c) -√ 3 ⁄2
d) √ 3 ⁄2
e) 1⁄2
f) None of the above.
14) Evaluate: sec 
π⁄
6
a) √ 3 ⁄3
*b) 2 √ 3 ⁄3
c) 2
d) -2 √ 3 ⁄3
e) − 2
f) None of the above.
15) Given that sin ( x )  =  1⁄8 with 90° < x < 180°, and sin ( y )  =  − 7⁄9 with 180° < y < 270°. Find sin ( x − y ) .
a) √ 14 ⁄6 − 7⁄72
b) -√ 2 ⁄18 +
7√ 7 ⁄
24
c) -√ 2 ⁄18
*d) -√ 2 ⁄18 −
e)
√ 14 ⁄
6
+
7√ 7 ⁄
24
7⁄
72
f) None of the above.
16) Find the exact value of the following expression. Do not use a calculator. If undefined, state Undefined.
arccos 
√ 3 ⁄
2
a) -π⁄3
b) -π⁄6
c) Undefined
*d) π⁄6
e) π⁄3
f) None of the above.
17) Find the exact value of the following expression. Do not use a calculator. If undefined, state Undefined.
csc  cos -1 
4⁄
5
a) 4⁄3
b) Undefined
c) 3⁄4
*d) 5⁄3
e) 3⁄5
f) None of the above.
18) Suppose that  θ  is an acute angle of a right triangle and that sec (θ)  =  12⁄7 . Find sin (θ) and cot (θ).
a) sin (θ)  =  12⁄7 , cot (θ)  =  12 √ 95 ⁄95
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b) sin (θ)  =  12 √ 95 ⁄95 , cot (θ)  =  7 √ 95 ⁄95
c) sin (θ)  =  7⁄12 , cot (θ)  =  √ 95 ⁄12
*d) sin (θ)  =  √ 95 ⁄12 , cot (θ)  =  7 √ 95 ⁄95
e) sin (θ)  =  √ 95 ⁄12 , cot (θ)  =  √ 95 ⁄7
f) None of the above.
19) Find the amplitude for the following function:
a) π⁄4
b) 1
*c) 2
d) π⁄2
e) 4
20) Which of these is an equation of one of the asymptotes of the following function?
a) x  =  1⁄8
*b) x  =  1⁄2
c) x  =  5
d) x  =  1⁄4
e) x  =  1⁄6
f) None of the above.
21) Find the phase shift for the following function:
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a) π left
b) π right
*c) 3 left
d) 3 right
e) 4 left
22) Find the period for the following function:
a) − 1
b) π⁄4
*c) π⁄2
d) 1⁄4
e) 4
f) None of the above.
23) In triangle ABC, ∠A measures 33°. If ∠C measures 76° and BC has length 7, find AB.
a)
b) 7⁄2
c) 7√ 3 ⁄2
*d)
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e)
f) None of the above.
24) Find the area of triangle XYZ if ∠Y = 30° , z = 9 and x = 5.
a) 45√ 3 ⁄4
*b) 45⁄4
c) 45√ 3 ⁄2
d) 25⁄4
e) 45⁄2
f) None of the above.
25) Given  csc ( x )  =  − 8 with 270° <  x  <  360°. Find  cos ( 2 x ).
a) 1⁄8 · (3√ 7  − 1)
*b) 31⁄32
c) 1
d) 63⁄64
e) − 2
f) None of the above.
26) Use the appropriate angle-sum formula to simplify the following expression:
cos (8 x) cos (7 x) −  sin (8 x) sin (7 x)
a) cos (56 x)
b) cos (x)
*c) cos (15 x)
d) sin (15 x)
e) sin (x)
f) None of the above.
27) Evaluate:
sin 
-π⁄
3
a) -√ 3 
*b) -√ 3 ⁄2
c) 1⁄2
d) √ 3 ⁄2
e) − 1⁄2
f) None of the above.
28) Suppose that you are headed toward a plateau 40 meters high. If the angle of elevation to the top of the plateau is 27°,
how far are you from the base of the plateau?
a) 40sin(27°)
b) 40⁄sin(27°)
*c) 40⁄tan(27°)
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d) 40cos(27°)
e) 40tan(27°)
f) None of the above.
29) Evaluate: sin (315°)
a) -√ 3 ⁄2
b) √ 3 ⁄2
c) √ 2 ⁄2
*d) -√ 2 ⁄2
e) 1⁄2
f) None of the above.
30) Given triangle ABC with AB = 3 and BC = √ 6  . The measure of angle A is 45°. How many choices are there for the
measure of angle C?
a) 3
b) 1
c) 4
d) 0
*e) 2
f) None of the above.
31) Solve sin (6x) = 1 on the interval [ 0 , π⁄2 ] .
a) x  =  π⁄3 , x  =  4π
*b) x  =  π⁄12 , x  =  5π⁄12
c) x  =  π⁄2
d) x  =  π⁄12 , x  =  π⁄4
e) x  =  π⁄12
f) None of the above.
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