sample_midterm-2

sample_midterm-2 - (b f x = 1 x 2 − 4 x 3 6 Sketch the...

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Mathematical Functions Sample Midterm Exam In the following problems you are required to show all your work and provide the necessary explana- tions everywhere to get full credit. 1. Find all real solutions of the following equations: (a) x 2 3 x 8 = 0 (b) x + 1 x 2 = x + 1 (c) x 1 / 3 3 x 1 / 6 + 2 = 0
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2. Solve the following inequalities. Express the solutions using interval notation and graph the solution sets. (a) x 2 + x 12 (b) x + 2 2( x 3) > x 1 (c) | 2 x 1 | > 1
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3. Helen earns $8 . 00 per hour at her job, but if she works more than 35 hours in a week she is paid 1 1 2 times her regular wage for the overtime hours worked. One week her gross pay was $400 . 00 . How many overtime hours did she work that week? 4. Find an equation of the line through the points (3 , 2) and ( 1 , 4) .
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5. Find the domain of the following functions. Express the solutions using interval notation . (a) f ( x ) = ( x 1)( x + 2)( x + 4)
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Unformatted text preview: (b) f ( x ) = 1 x 2 − 4 x + 3 6. Sketch the graph of the piecewise defined function f ( x ) = x 2 if x < 1 x 3 if x ≥ 1 and find f (0) , f (1) , f (2) . 7. Sketch the graph of the function f ( x ) = −| x − 1 | + 2 , not by plotting points, but by starting with the graph of a standard function and applying transformations. 8. Show that the equation x 2 + y 2 + 8 x − 4 y + 3 = 0 represents a circle, and find the center and radius of the circle. 9. Find the maximum or minimum value of the function y = x 2 − 2 x + 2 . 10. Use f ( x ) = √ 1 − x and g ( x ) = 1 x 2 + 1 to find (a) f ◦ g (b) g ◦ f (c) f ◦ f (d) g ◦ g (e) fg (f) f/g 11. Find the inverse of the following functions: (a) f ( x ) = x x − 2 (b) f ( x ) = 1 + 2 x 3...
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This note was uploaded on 02/27/2012 for the course MATH 8650 taught by Professor Kiryltsishchanka during the Spring '12 term at NYU.

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sample_midterm-2 - (b f x = 1 x 2 − 4 x 3 6 Sketch the...

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