OptionalQuiz_Fall2009

OptionalQuiz_Fall2009 - e ) + ln( e 3 )-ln( e 4 ) + log 2 4...

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MAP 103: Proficiency Algebra, Optional Quiz, Fall 2009 Answer 5 questions at 20 points each or 10 questions at 20 points each. Show all work. 1. Solve for x : 4 x + 7 · 4 x = 8 . 2. Let f ( x ) = ln( x + 1) ,g ( x ) = ln x, and h (ln 2) = e 2 . Find f g h (ln 2) . 3. Solve for x and check: log 4 x + log 4 x 3 = 2 . 4. Let f ( x ) = 2 ln(2 x - 1) . Sketch a graph for f ( x ) and state the domain. 5. Write the equation of an exponential function f ( x ) = ab x such that f (0) = 4 and f (2) = 72 . Using f ( x ) , find f (4) . 6. Express y as a function of x : log 3 y = 2 + 4 log 3 (2 x ) . 7. Find in exact value the expression: 5 2 log 2 32 . 8. Solve for x : 2 3 x = 16 2 . 9. Solve for x : e 5 x - e 3 x - e 2 x + 1 = 0 . 10. Express in simplest form: log 3 4 s x 9 y 81 z 3 w , where x,y,z,w > 0 . 11. Evaluate: ln(
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Unformatted text preview: e ) + ln( e 3 )-ln( e 4 ) + log 2 4 + log 2 2 2 2 + log 8 1 + log 64 4 + log 3 3 2 . 12. Find the equation of the line that passes through the point (1 ,-1) and is perpendicular to the line y =-kx + 1 . Here k > . 13. Let f ( x ) = x 2 + 3 x-4 x 4-17 x 2 + 16 . Sketch a complete graph of f ( x ) including points of discontinuity, asymptotes, zeros, and y-intercept. 14. Factor completely: x 6-14 x 4 + 49 x 2-6 = 0 and list the roots. 15. Find the degree: x 4 y 6-y 5 x 3 + x 2 y 4-y 3 x + y 4 ....
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