### About Functions Vertical Line Test:

A relation is any set of ordered pairs (x,y). A function is a special type of relation where there is a one to one correspondence. Each first component or x-value corresponds to or is linked to exactly one second component or y-value. Many times, we hear this read as "for each x, there can be only one y". When we have a function, no vertical line will intersect the graph in more than one location.

Test Objectives

- Demonstrate an understanding of the concept of a function
- Demonstrate an understanding of domain and range
- Demonstrate the ability to use the vertical line test to determine if a relation represents a function

#1:

Instructions: determine if each relation is a function.

$$a)\hspace{.2em}y=-\frac{1}{2}x + 2$$

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#2:

Instructions: determine if each relation is a function.

$$a)\hspace{.2em}|y|=x + 2$$

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#3:

Instructions: determine if each relation is a function.

$$a)\hspace{.2em}y=(x - 6)^2 + 1$$

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#4:

Instructions: determine if each relation is a function.

$$a)\hspace{.2em}y=x^3 - x$$

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#5:

Instructions: determine if each relation is a function.

$$a)\hspace{.2em}(x + 2)^2 + y^2=36$$

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Written Solutions:

#1:

Solutions:

a) Function

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#2:

Solutions:

a) Not a Function

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#3:

Solutions:

a) Function

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#4:

Solutions:

a) Function

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#5:

Solutions:

a) Not a Function