mathematics

MATH 112 Fall 2018 - GHW 2 Part 4 (updated) Name _________________________________________________ This GHW is due at the beginning of class on Wednesday, October 10. We didn’t get as far as I had hoped to in class on Monday so I reduced the problem set from 5 to 3 problems. You may discuss this assignment with others in the class or with me, but the work that you turn in must be your own write-up. For each of the following problems, supporting work is necessary for credit (unless stated otherwise). Supporting work must be presented in a complete, neat and orderly fashion. This includes the use of correct notation. Put your work and answers (unless stated otherwise) on one side of separate standard size sheets of paper. Your work must be stapled (in the upper left-hand corner) to this sheet with this sheet being the first page, and with the problems given in order. Be sure to justify and simplify your answers. Remember to use pencil. Express all numerical answers using exact values. Be sure to label quantities, use equal signs appropriately and give a conclusion.

1. Simplify 5

(3 4 )(3 2 )i i  by putting it in the standard form a bi .

2. Let 2( ) 3 4 4f x x x   .

No supporting work is necessary for parts a), c), d), g) and h). a) Determine the domain of f. b) Express f in standard form by using the process of completing the square. c) Using the results of b), determine the vertex of the graph of f. d) Determine the range of f. e) Determine the x intercept(s) of the graph of f, if any. List as ordered pairs. f) Determine the y intercept(s) of the graph of f, if any. List as ordered pairs. g) Determine the axis of symmetry of the graph of f. Give the answer as an equation. h) Determine the intervals where the function f is increasing and decreasing (recall we use open intervals).

Express your answer(s) using interval notation. i) Determine the maximum and minimum values of f, if they exist.

Justify your answer and be sure to address both the maximum and minimum values.

3. Determine the domain of the function 2

2 1 ( )

6 15

x f x

x x

 

  . Express the domain using interval notation.