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Representing Functions. TLW determine whether a relation is a function; find functional values. TEKS: A.4A, A.4C, A.5C. Determine whether the relation {(6, -3), ( 4, 1), (7, -2), (-3, 1)} is a function. Explain.

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Representing functions

Representing Functions

TLW

determine whether a relation is a function; find functional values.

TEKS: A.4A, A.4C, A.5C


Representing functions

  • 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 oneelement of the range, this relation isafunction.


Representing functions

Since the element 2 in the domain is paired with both 5 and 4 in the range, this table doesnot represent afunction.


Representing functions

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.


Now your turn are the following relations considered functions
Now your turn…Are the following relations considered functions?

  • {(-3, -3), (-3, 4), (-2, 4), (0, 6)}

No

Yes

x

y

-1

4

0

5

No

1

6

2

7


Representing functions

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.


Now your turn are the following graphs considered functions
Now your turn …Are the following graphs considered functions?

Yes

3x – y = 6

Yes

x = -4

No

y = 3

Yes


Representing functions

Equations that are functions can be written in a form called function notation. For example…Equation: y = 3x – 8 Function Notation: f(x) = 3x – 8 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


Once again your turn if f x 2x 4 and g x x 2 4x find each value
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


Real world problem
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