1. A relation can be expressed in three ways.  Name them.

 i.   _EQUATION_______

 ii.  __GRAPH________

 iii .___ORDERED PAIRS________
 

2.  Define Function.

A function is a special relation in which every value of x is associated with only one value of y.

3. Give the domain and range of the function, f(x) = 4 |x-2| +3

 Domain : x e R

 Range   : y => 3, y e R
 

4. Give the inverse of the following functions.
 a)    f(x) = {(0,3), (2,5), (3, 6)}                       f ^-1(x) = {(3,0), (5,2), (6,3)}

 b)    f(x) =  ² / _(x-5) + 3                                      f ^-1(x) = ² / _(x-3) + 5
        rewrite f(x) as y
         y =   ² / _(x-5) + 3

         switch x with y, and y with x.

        x =  ² / _(y-5) + 3

        solve for y

        x - 3 = ² / _(y-5)

        (x-3)(y-5) = 2

        y - 5 = ² / _(x-3)

        _{y =} ² / _(x-3) + 5
 

c)

The graph is reflected on the line y = x.
 

 5. Sketch y =  SQRT(x-6)  + 3   (the square root of x-6)

6. Sketch y = 2 Int (2x)

7. If m(x) = 3x-7,
 a) Evaluate m(5)

m(x) = 3x-7
m(5) = 3(5) -7
        = 15 -7
        = 8

 b) Evaluate m(x-5)

m(x) = 3x - 7
m(x-5) = 3(x-5) - 7
         = 3x - 15 - 7
        =  3x - 22

8) If b(x) = 2x², and n(x) = 4x-5, evaluate b(n(x)) and n(b(x)).

b(x) = 2x²
b(n(x)) = 2 (n(x)) ²
        = 2 (4x-5)²
        = 2 (16x²  - 40x + 25)
        = 32x²  - 80x + 50

n(x) = 4x - 5
 n(b(x)) = 4(b(x)) - 5
        = 4 (2x² ) - 5
        = 8x²  - 5

9) If t(x) =4 |x-3| and b(x) = x² - 5, evaluate 2t(4) - 3b(-2)

2t(4) - 3b(-2)
2(4 |(4)-3| ) - 3((-2)² -5)
2(4 | 1 | ) - 3(4 - 5)
2(4 (1) ) - 3(-1)
2(4) + 3
8 + 3
11