MATH 121 Extra Problems for 2.2 through 3.1

1.) Suppose f(x) is the function defined by the following graph. Draw g(x) on the same graph where g(x) = 2f(x+3) - 1 .

2.) Decide if each of the following function is odd, even, or neither.

(a.)

 

 (b.)
(c.)

 

 (d.)

 

 

For number 3, if a graph looks close to being symmetric, assume that it is, some printers move parts of pictures slightly.

3.) Label the graphs below with the letters of all of the following that apply:
a. Symmetric with respect to the x-axis
b. Symmetric with respect to the y-axis
c. Symmetric with respect to the origin
d. Not symmetric with respect to the x-axis, y-axis, nor the origin

A.)

 B.)
C.)

 D.)
E.)

 F.)
G.)

 H.)
I.)

 J.)

4.) Label the equations below with the letters of all of the following that apply to their graphs:
a. Symmetric with respect to the x-axis
b. Symmetric with respect to the y-axis
c. Symmetric with respect to the origin
d. Not symmetric with respect to the x-axis, y-axis, nor the origin

Show any work needed to come to your conclusions.

A.)

 

 

 

 

 

 

 

 B.)
C.)

 

 

 

 

 

 

 

 D.)
E.)

 

 

 

 

 

 

 F.)

5.) Let f(x) be defined by the following set of ordered pairs: {(-2, 0), (0, 2), (1, -2), (3, 1)} Find the set of ordered pairs that represents:

    1. g(x) if g(x) = -f(x + 2) +1
    2. h(x) if h(x) = f(x/2)
    3. k(x) if k(x) = ½ f(x) + 1

6.) For each of the following draw in the minimum number of points needed to represent...

an even function

 an odd function

7.) Match the equations to their graphs below. Choose the best answer. Assume the scale on each graph is the same. Assume a is a positive constant. Should be able to do quickly without a calculator.

f(x) = |x| _____ g(x) = |x + a| _____ h(x) = |x – a| _____
j(x) = |x| + a ______ k(x) = a|x| ______ l(x) = -|x| – a _____
a)

b)
c)

 d)
e)

 f)

8.) Suppose a hose can fill a pool by itself in 12 hours. A smaller hose takes 15 hours to fill the pool. Suppose you are filling the pool with the larger hose for 3 hours when you add the smaller hose. How long will it take to finish filling the pool?

9.) Let g(x) = x2 + 2x .  Find and simplify.

10.) Let . Find:

(a.) f(½ ) (b.)
(c.) dom f (d.) dom g
(e.) (f.)

11.) Let . Write f(x) in terms of h(x), g(x), and l(x).

12.) Let   and   g(x) = x2 + 2x, evaluate:

(g.)    (h.)

13. Let f(x) and g(x) be defined as in the following charts:

Find:
 f(3)

14.) The diameter d of a cube is the distance between two opposite vertices. Express d as a function of the edge x of the cube. (Hint: First express the diagonal y of a face as a function of x.)

15.)  Simplify the following. Put your answer in the form a + bi where a and b are reals.

  1. 6i(5 + 3i)
  4. i291
  5. (-i)651
  6. -i348

16.) Use the following graph to fill in the blanks.
(g o f)(0) = ______

dom (g o f) = ___________________

Solutions:

1.)

2.)   a.) odd,   b.) even,   c.) neither,   d.) even

3.) A.) b   B.) d   C.) d   D.) d   E.) a   F.) d   G.) d   H.) c   I.) a, b, c   J.) b

4.)   A.) b   B.) c   C.) a, b, c   D.) a   E.) d   F.) a

5.)   a) {(-4, 1), (-2, -1), (-1, 3), (1, 0)}
    b) {(-4, 0), (0, 2), (2, -2), (6, 1)}
    c) {(-2, 1), (0, 2), (1, 0), (3, 3/2)}

6.) an even function

 an odd function

7.) f – a,     g –     f,     h – c,     j – e,     k – b,     l - d

8.) 5 hours

9.) 2x + 2 + h

10.) a.) 1     b.)     c.) (-infin; , 0) ∪ (0, ∞)    d.) (-∞, 1) ∪ (1, ∞)    e.) does not exist    f.) (-∞, 0) ∪ (0, ½) ∪ (½, ∞)

11.) f(x) = h(g(x)) + l(x)

12.) a.) 2,     b.) -2,     c.) 0,     d.) 3,     e.) 0,     f.) -x2+2x,     g.) -2,     h.) 0

13.) 7, -4, 8, & 5 respectively

14.)

15.) Simplify the following. Put your answer in the form a + bi where a and b are reals.

  1. -18 + 30i
  2. 13i

  4. , so since the remainder is 3:i291 = i3 = -i
  5. 1
  6. -1

16.) (g o f)(0) = 3
dom (g o f) = [0, 4]