Determine if a Relation is a Function - Pre-Calculus
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Which of the following expressions is not a function?
Which of the following expressions is not a function?
Recall that an expression is only a function if it passes the vertical line test. Test this by graphing each function and looking for one which fails the vertical line test. (The vertical line test consists of drawing a vertical line through the graph of an expression. If the vertical line crosses the graph of the expression more than once, the expression is not a function.)
Functions can only have one y value for every x value. The only choice that reflects this is:
Recall that an expression is only a function if it passes the vertical line test. Test this by graphing each function and looking for one which fails the vertical line test. (The vertical line test consists of drawing a vertical line through the graph of an expression. If the vertical line crosses the graph of the expression more than once, the expression is not a function.)
Functions can only have one y value for every x value. The only choice that reflects this is:
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Suppose we have the relation 
on the set of real numbers 
whenever 
. Which of the following is true.
Suppose we have the relation
The relation is not a function because 
and 
hold. If it were a function, 
would hold only for one 
. But we know it holds for 
because 
and 
. Thus, the relation 
on the set of real numbers 
is not a function.
The relation is not a function because
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Consider a family consisting of a two parents, Juan and Oksana, and their daughters Adriana and Laksmi. A relation 
is true whenever 
is the child of 
. Which of the following is not true?
Consider a family consisting of a two parents, Juan and Oksana, and their daughters Adriana and Laksmi. A relation
The statement
"Even if the two parents had only one daughter, the relation would not be a function."
is not true because if they had only one daughter, say Adriana, then the only relations that would exist would be (Juan, Adriana) and (Oksana,Adriana), which defines a function.
The statement
"Even if the two parents had only one daughter, the relation would not be a function."
is not true because if they had only one daughter, say Adriana, then the only relations that would exist would be (Juan, Adriana) and (Oksana,Adriana), which defines a function.
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Which of the following relations is not a function?
Which of the following relations is not a function?
The definition of a function requires that for each input (i.e. each value of 
), there is only one output (i.e. one value of 
). For 
, each value of 
corresponds to two values of 
(for example, when 
, both 
and 
are correct solutions). Therefore, this relation cannot be a function.
The definition of a function requires that for each input (i.e. each value of
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Given the set of ordered pairs, determine if the relation is a function
Given the set of ordered pairs, determine if the relation is a function
A relation is a function if no single x-value corresponds to more than one y-value.
Because the mapping from 
goes to 
and 
the relation is NOT a function.
A relation is a function if no single x-value corresponds to more than one y-value.
Because the mapping from
the relation is NOT a function.
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What equation is perpendicular to 
and passes throgh 
?
What equation is perpendicular to
First find the reciprocal of the slope of the given function.
The perpendicular function is:
Now we must find the constant, 
, by using the given point that the perpendicular crosses.
solve for 
:
First find the reciprocal of the slope of the given function.
The perpendicular function is:
Now we must find the constant,
solve for
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Is the following relation of ordered pairs a function?
Is the following relation of ordered pairs a function?
A set of ordered pairs is a function if it passes the vertical line test.
Because there are no more than one corresponding 
value for any given 
value, the relation of ordered pairs IS a function.
A set of ordered pairs is a function if it passes the vertical line test.
Because there are no more than one corresponding
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