Question

Are all lines function? Explain.

Why does the vertical line test work?

How can you determine whether a relation is a function when the relation is represented as a set of ordered pairs?

How can you evaluate a function for a given value when the function is represented as a graph?

Please answer ALL these questions in order from 1 to 4. This is not part of the question, just letting you know.

Answer 1

1.  Not all lines represent functions.  A vertical line, for example, does not have a defined slope due to division by zero.  Otherwise, all straight lines represent functions.

2.  If a relationship shows two or more y-values for any given x-value, then that relationship is NOT a function.  If you graph such a relationship and then draw a vertical line thru your graph, and see that the line intersects the graph more than once, you know your rel. is not a function.

3.  Refer back to #1.  If any one x-value is associated with more than one y-value, the relationship is NOT a function.

4.  Draw a vertical line thru the input (x-) value at which you wish to evaluate the function.  What is the y-value at the point of intersection of this line and the graph?  

Answer 2

all lines are not functions....a function will not have any repeating x values. it can have repeating y values, just not the x ones.
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To determine if ur line is a function, there is the vertical line test. if u run a vertical line through the line on the graph, if ur line on the graph touches the vertical line more then once, it is not a function.
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if u get a set of ordered pairs, such as { (2,3),(3,4),(4,5),(6,7)}...to determine if this is a function just by looking at it, just look at ur x values. If all ur x values are different, then it is a function....so this one is a function.

But...{ (2.3), (2,4), (3,4), (4,5)}...this is not a function because it has 2 x values that are the same....u have two x values that are both 2.
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example :....lets say u have a line on ur graph....and u get something like 
h(-4).....this is basically saying x = -4......so u would look at ur graph and find the point where x is -4 and see what y equals. 
I am not sure how to explain this one.....so ur h(-4) would be equal to the y value of the (-4,y) point