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Algebra 4-6 Functions Functions A function is a relation in which each element of the domain is paired with exactly one element of the range. Functions Harbour

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Identify Functions Determine whether the relation is a function. Explain. Answer: This is a function because the mapping shows each element of the domain paired with exactly one member of the range. Example 6-1a

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Identify Functions Determine whether the relation is a function. Explain. x y –7 –12 –4 –9 2 –3 5 Answer: This table represents a function because the table shows each element of the domain paired with exactly one element of the range. Example 6-1b

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Identify Functions Determine whether {(–5, 2), (–2, 5), (0, 7), (0, 9)} is a function. Explain. Answer: This relation is not a function because the element 0 in the domain is paired with both 7 and 9 in the range. Example 6-1c

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Identify Functions Determine whether each relation is a function. Explain. a. Answer: This mapping represents a function since, for each element of the domain, there is only one corresponding element in the range. Example 6-1d

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**Identify Functions Y X b. c. {(3, 0), (1, 2), (4, 0), (5, –1)} –1 3 –4**

–2 1 Y X Answer: This relation is not a function because the element 3 in the domain is paired with both 2 and –1 in the range. Answer: This is a function because the mapping shows each element of the domain paired with exactly one member of the range. Example 6-1d

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Algebra 4-6 Functions Functions You can use the vertical line test to see if a graph represents a function. If no vertical line can be drawn so that it intersects the graph no more than once, then the graph is a function. If a vertical line can be drawn so that it intersects the graph at two or more points, the relation is not a function. Functions Harbour

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**One way to perform the vertical line test is to use a pencil.**

Algebra 4-6 Functions Functions One way to perform the vertical line test is to use a pencil. Functions Harbour

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**Equations as Functions**

Determine whether is a function. Graph the equation. Since the graph is in the form the graph of the equation will be a line. Place your pencil at the left of the graph to represent a vertical line. Slowly move the pencil to the right across the graph. At this vertical line passes through more than one point on the graph. Answer: The graph does not pass the vertical line test. Thus, the line does not represent a function. Example 6-2a

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**Equations as Functions**

Determine whether is a function. Answer: yes Example 6-2b

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**equation function notation**

Functions Algebra 4-6 Functions Equations that are functions can be written in a form called function notation. equation function notation range domain Functions Harbour

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**Function Values If find . Replace x with 4. Multiply. Subtract.**

Answer: Example 6-3a

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**Function Values If find . Replace x with –5. Multiply. Subtract.**

Answer: Example 6-3b

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**Function Values If find . Replace x with 2 – x. Distributive Property**

Simplify. Answer: Example 6-3c

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**Function Values If find each value. a. b. Answer: 11 c. Answer: –11**

Example 6-3d

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**Some functions are not linear. **

However, you can still find values of these functions. Nonlinear Function Values If , find . Replace m with –3. Multiply. Simplify. Answer: Example 6-4a

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**Nonlinear Function Values**

If , find . Replace m with 6z. Simplify. Answer: Example 6-4b

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**Nonlinear Function Values**

If , find . Evaluate k(y) by replacing m with y. Multiply the value of k(y) by –4. Simplify. Answer: Example 6-4c

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**Nonlinear Function Values**

If find each value. a. b. c. Answer: 8 Answer: Answer: Example 6-4d

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**Nonstandard Function Notation**

Multiple-Choice Test Item A B C D 81 If Read the Test Item The symbol is just a different notation for f(x). Solve the Test Item Replace x with –5. Think: . Replace x with –5. Simplify. Answer: A Example 6-5a

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**Nonstandard Function Notation**

Multiple-Choice Test Item A B C D 19 If Answer: C Example 6-5b

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