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# big_review - Fall 2007 Math 120 Section 5 Final Exam...

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Fall 2007 Math 120, Section 5 Final Exam Practice Disclaimer: These problems are not intended to be a comprehensive review of the course. You should review all your class notes, homework (collected and uncollected), previous exams, previously suggested review problems, etc. 1 Problem One For each of the following functions, state whether the function is linear, quadratic, a polynomial (and state the degree if so), power, rational, exponential, logarithmic, trigonometric, a composition of any of these, or none of these. 1. f ( x ) = x 2 ( x 3 - 1) 1 / 2 - x - 1 ( x 3 - 1) - 1 / 2 x 3 - 1 . 2. f ( x ) = 3 cos 2 x + 3 sin 2 x + x 2 - 2 x + 1 . 3. f ( x ) = 3 · 2 x 4. f ( x ) = 2 sin 2 x 5. f ( x ) = 3 log b ( x - 3) + 7 6. f ( x ) = 3 7. f ( x ) = 3 x 4 - 5 x 2 + 1 x - 3 - 1 7 . 8. f ( x ) = πx e 9. f ( x ) = x - 3 10. f ( x ) = x π 11. f ( x ) = x x 12. f ( x ) = e e e x 2 Problem Two The expression n ! for a positive integer n means n ( n - 1)( n - 2) ··· (2)(1) and is read “ n -factorial,” and we simply deﬁne 0! = 1 . Simplify the following expressions: 1. 2 n +1 ( n + 1)! 2 n n ! . 2. n X i =1 ln i.

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3 Problem Three Graph each of the following functions. Label all relevant features (asymptotes, intercepts, etc.) 1. f ( x ) = P 0 e αx - β where P 0 , α and β are ﬁxed positive constants. 2. f ( x ) = 2 x 2 - 5 x + 3 3. f ( x ) = 2 ln ( x - 1) + 3 4. f ( x ) = - 2( x 2 - 25)( x + 4) 2 ( x - 7) 5 5. f ( x ) = - 3 x + 7 6. f ( x ) = 10 , 674 7. f ( x ) = 3 sin (2 π ( x - 3)) + 7 8. f ( x ) = sec 2 x - tan 2 x - 1 9. f ( x ) = x 2 - 5 x + 6 2 x 2 - 12 x + 16 10. f ( x ) = 7 cos 6( x + 2) - 2 11. f ( x ) = x 3 - 2 x 2 + x 12. f ( x ) = - 2 x 2 + 1 x - 1 13. f ( x ) = 3e - x 14. f ( x ) = 2 log 2 ( - x ) 4 Problem Four Find a possible formula for each of the following graphs:

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5 Problem Five Which of the following represent functions? For those that represent functions, which might have inverse functions? Justify your answers. t -7 11 17 37 101 α 123 983 456 98 π y - e π + e e π 5670 e e e 57289141 x -1 345 2/7 - 1 π π + e
α -2 -1 0 -1 β 23 81 1 0 6 Problem Six Find the domain of each of the following functions. 1.

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big_review - Fall 2007 Math 120 Section 5 Final Exam...

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