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A practice exam for math 1050, focusing on topics such as polynomials, functions, and inequalities. It includes multiple-choice questions, fill-in-the-blank exercises, and problem-solving tasks. Students are expected to determine if statements are true or false, fill in missing information, identify function properties, and graph equations.
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Exam 1 practice, Math 1050 (100 pts total), Name:
(10 pts) 1. True or False. ( ) (a) A polynomial of degree n can have at most n − 1 x-intercepts.
( ) (b) If f (x) = x^3 + 5, then f (x + 2) = (x + 2)^3 + 5.
( ) (c) The graph of an odd function has no symmetry.
(10 pts) 2. Fill in the blanks. (a) The graph of g(x) = |x + 3| − 5 is the same as the graph of f (x) = |x| except
(b) The domain of the function f (x) = (^) x−^15 is
(c) The graph of the solution set of the absolute value inequality |x| ≤ 7 is
(10 pts) 3. Determine whether each of the following represents a function (y as a function of x). Write “yes” or “no” in the corresponding blanks. State your reason(s).
(a) (b)
(c) (d)
(a) (b) (c) (d)
Reasoning:
(10 pts) 4. Determine whether each of the following functions is odd, even, or neither.
(10 pts) 7. A farmer has 500 feet of fencing. He would like to build a rectangular enclosure with that is divided into three pieces (as shown in the picture on the right). What is the greatest total area (all three pieces together) that he can create? (For full credit, you’ll need to complete the square, but you can earn partial credit by using a formula that you may know.)
and label three points on this new graph. (Note: the left point should be labeled (-2, 1).)
(10 pts) 9. Solve the equation | 5 x − 6 | = 13.
(10 pts) 10. Sketch the graph of f (x) = (^) x(x^1 −2) 2 by finding its x and y intercepts, asymptotes, and plotting at least three additional points. Note: Show all your work!
