1. Representing Functions
TLW
determine whether a relation is a function; find functional values.
TEKS: A.4A, A.4C, A.5C

2. Determine whether the relation
{(6, -3), ( 4, 1), (7, -2), (-3, 1)} is a function. Explain.
Since each element of the domain is paired with exactly one element of the range, this relation is a function.

3. Determine whether the relation is a function. Explain. x -3 2 3 y 6 5 1 4
Since the element 2 in the domain is paired with both 5 and 4 in the range, this table does not represent a function.

4. Determine whether the relation is a function. Explain.y x -4 9 -1 -6 1 11 3
For each element in the domain, there is only one corresponding element in the range. So, this mapping represents a function.
**It does not matter if two elements of the domain are paired with the same element in the range.

5. Now your turn… Are the following relations considered functions?
{(-3, -3), (-3, 4), (-2, 4), (0, 6)} No x 4 -1 1 y -5
-10 -9 -7
Yes x y -1 4 5 No 1 6 2 7

6. Determine if the following graphs are functions. Explain.
Use the Vertical Line Test to determine if a graph represents a function. If the vertical line intersects (touches) the graph only once, then the graph does represent a function. If the vertical line intersects (touches) the graph at two or more points, then the graph does not represent a function.
Determine if the following graphs are functions. Explain.
If you draw a vertical line through the graph, the vertical line passes through two points. Thus, the graph does not represent a function.
If you draw a vertical line through the graph, the vertical line passes through just one point. Thus, the graph does represent a function.
If you draw a vertical line through the graph, the vertical line passes through two points at x=1. Thus, the graph does not represent a function.

7. Now your turn … Are the following graphs considered functions?
Yes
3x – y = 6
Yes
x = -4 No
y = 3
Yes

8. If f(x) = 3x – 4, find the value. a.) f(3)
Equations that are functions can be written in a form called function notation. For example… Equation: y = 3x – Function Notation: f(x) = 3x – or g(x) = 3x – 8 , etc.
If f(x) = 3x – 4, find the value.
a.) f(3)
b.) f(-2)
f(3) = 3(3) – 4
= 9 – 4
= 5
f(-2) = 3(-2) – 4
= -6 – 4
= -10

9. f(0) = g(-3) = f(3x) = f(½) = g(-4) + 3 =
Once again, your turn… If f(x)=2x – 4 and g(x)=x2 – 4x. Find each value.
f(0) =
g(-3) =
f(3x) =
f(½) =
g(-4) + 3 = -4 21
6x - 4 -3 35

10. It costs $1.25 to send 5 photos and $3.00 to send 12 photos.
Real World Problem
The cost of sending cell phone pictures is given by y=0.25x, where x is the number of pictures that you send. Write the equation in function notation and then find f(5) and f(12). What do these values represent?
f(x) = 0.25x
It costs $1.25 to send 5 photos and $3.00 to send 12 photos.
f(5) = 1.25
f(12) = 3