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sample_midterm-1

# sample_midterm-1 - x 2 y 2 2 x-4 y 2 = 0 represents a...

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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. I. (20 points) Find all real solutions of the following equations: (a) 2 x 2 - 3 x - 4 = 0 (b) x + 3 - x = 1

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II. (10 points) Solve the following nonlinear inequality and express the solution using interval notation: 2 x + 3 4 - 2 x 0 III. (10 points) 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?
IV. (10 points)

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Unformatted text preview: x 2 + y 2 + 2 x-4 y + 2 = 0 represents a circle, and ﬁnd the center and radius of the circle. V. (10 points) Find an equation of the line through the points (1 , 2) and (2 ,-1) . VI. (20 points) Find the domain of the following functions: (a) f ( x ) = x 3 x-7 (b) g ( x ) = √ x 2 + x-2 VII. (10 points) Sketch the graph of the piecewise deﬁned function f ( x ) = x 2-5 if x ≤ -2 1-x if x >-2 VIII. (10 points) Sketch the graph of the function f ( x ) =-2-| 3-x | , not by plotting points, but starting with the graph of a standard function and applying transformations....
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