Understanding Functional Notations - High School Math
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Which analysis can be performed to determine if an equation is a function?
Which analysis can be performed to determine if an equation is a function?
The vertical line test can be used to determine if an equation is a function. In order to be a function, there must only be one 
(or 
) value for each value of 
. The vertical line test determines how many 
(or 
) values are present for each value of 
. If a single vertical line passes through the graph of an equation more than once, it is not a function. If it passes through exactly once or not at all, then the equation is a function.
The horizontal line test can be used to determine if a function is one-to-one, that is, if only one 
value exists for each 
(or 
) value. Calculating zeroes, domain, and range can be useful for graphing an equation, but they do not tell if it is a function.
Example of a function: 
Example of an equation that is not a function: 
The vertical line test can be used to determine if an equation is a function. In order to be a function, there must only be one
The horizontal line test can be used to determine if a function is one-to-one, that is, if only one
Example of a function:
Example of an equation that is not a function:
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Evaluate 
if 
and 
.
Evaluate
This expression is the same as saying "take the answer of 
and plug it into 
."
First, we need to find 
. We do this by plugging 
in for 
in 
.
Now we take this answer and plug it into 
.
We can find the value of 
by replacing 
with 
.
This is our final answer.
This expression is the same as saying "take the answer of
First, we need to find
Now we take this answer and plug it into
We can find the value of
This is our final answer.
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Let 
and 
. What is 
?
Let
THe notation 
is a composite function, which means we put the inside function g(x) into the outside function f(x). Essentially, we look at the original expression for f(x) and replace each x with the value of g(x).
The original expression for f(x) is 
. We will take each x and substitute in the value of g(x), which is 2x-1.
We will now distribute the -2 to the 2x - 1.
We must FOIL the 
term, because 
.
Now we collect like terms. Combine the terms with just an x.
Combine constants.
The answer is 
.
THe notation
The original expression for f(x) is
We will now distribute the -2 to the 2x - 1.
We must FOIL the
Now we collect like terms. Combine the terms with just an x.
Combine constants.
The answer is
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If 
and 
, what is 
?
If
means 
gets plugged into 
.
Thus 
.
Thus
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Let 
and 
. What is 
?
Let
Calculate 
and plug it into 
.
Calculate
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