FinalExamQuestions - MAP 103 FINAL EXAM SAMPLE QUESTIONS...

MAP 103 FINAL EXAM SAMPLE QUESTIONS
(1) Express y as a function of x for the expression: log
3
y = 2 + 4 log
3
(2 x ) .
(2) Suppose f ( x ) =
√
x + 1 , g ( x ) = 2 x - 1 , and h (2) = 3 . Find f ◦ g ◦ h (2) .
(3) Let f ( x ) =
1
2
x -
1
3
. Write a formula for the inverse and check that f ◦ f
- 1
( x ) = x.
(4) Determine if the following are true or false. Circle T for true or F for false. If false, provide
a counter-example.
(a) T | F : log( a + b ) = log( a ) + log( b ) for a, b ≥ 0
(b) T | F : 2 x · 2 x = 2 2 x
(c) T | F : log
r
x 2 y 3
z 4
!
=
1
2
[log(2 x ) + log(3 y ) - log(4 z )]
(d) T | F : log( ab ) = log( a ) log( b ) for a, b ≥ 0
(5) Evaluate: log
2
2 + log
2
√
2 + log
2
2
2
+ log 2
1
2
.
(6) Let f ( x ) = x
2
+ 6 x + 9 .
(a) What are the coordinates for the vertex?
(b) How many values of x satisfy the equation f ( x ) = 0?
(c) What is the equation of the line that passes through the vertex that has slope 0?
(d) What is the new equation for f ( x ) after the transformation f ( x + 1) + 1?
(7) A catapult launches a rock into the air. The motion of the rock is modeled by the equation
m ( t ) = - 1000 t 2 +18000 t +26000 . Suppose that down range there is a castle with a defensive
wall 108 , 000 feet high.