Equations as Functions

							  Equations as Functions

Objective: To determine whether an
equation represents a function and
 find functional values for a given
             function.
              5-Minute Check
Write four solutions for each equation. Write the solutions
   as ordered pairs.
1. y = 2x – 4
                 5-Minute Check
Write four solutions for each equation. Write the solutions
   as ordered pairs.
1. y = 2x – 4

2. y = x/2 – 3
                 5-Minute Check
Write four solutions for each equation. Write the solutions
   as ordered pairs.
1. y = 2x – 4

2. y = x/2 – 3

3. x + y = 12
                 5-Minute Check
Write four solutions for each equation. Write the solutions
   as ordered pairs.
1. y = 2x – 4

2. y = x/2 – 3

3. x + y = 12

Determine whether each relation is linear.
4. x – y = 32
                 5-Minute Check
Write four solutions for each equation. Write the solutions
   as ordered pairs.
1. y = 2x – 4

2. y = x/2 – 3

3. x + y = 12

Determine whether each relation is linear.
4. x – y = 32

5. 25 – y2 = x2
   Equations as Functions


The solutions of an equation in two variables are
ordered pairs. Such an equation describes a
relation. The set of values of x is the domain of
the relation. The set of corresponding values of y
is the range.
           Equations as Functions
Example:
a. Solve y = 3x + 4 if the domain is {-2, -1, 0, 1}.   x    y
                                                       -2
                                                       -1
                                                       0
                                                       1
           Equations as Functions
Example:
a. Solve y = 3x + 4 if the domain is {-2, -1, 0, 1}.


b. Graph the equation.
           Equations as Functions
Example:
a. Solve y = 3x + 4 if the domain is {-2, -1, 0, 1}.


b. Graph the equation.


c. Is the equation a function?
   Equations as Functions


Equations that represent functions can be written
in functional notation, f(x). The symbol f(x) is
read “f of x” and represents the value in the range
that corresponds to the value of x in the domain.
For example, f(8) is the element in the range that
corresponds to the element 8 in the domain.
     Equations as Functions


One can determine a functional value by
substituting the given value for x into the equation.
 For example, if f(x) = 7x – 5 and x = 2, then
f(2) = 7(2) – 5 or 9.
     Equations as Functions


Assignment: 12 – 30 even, 32 – 40 all.
         Pages 394 – 395