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# Representing Functions - PowerPoint PPT Presentation

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

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.

Since each element of the domain is paired with exactly oneelement of the range, this relation isafunction.

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

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?

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

No

Yes

x

y

-1

4

0

5

No

1

6

2

7

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?

Yes

3x – y = 6

Yes

x = -4

No

y = 3

Yes

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)=x2 – 4x. Find each value.

f(0) =

g(-3) =

f(3x) =

f(½) =

g(-4) + 3 =

-4

21

6x - 4

-3

35

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