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**Representing Functions**

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

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**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.

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**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.

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**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.

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**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

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**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.

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

Yes 3x – y = 6 Yes x = -4 No y = 3 Yes

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**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

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**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

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**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

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