Special Functions - Pre-Calculus
Card 0 of 9
Which of the following is a point on the following function?
Which of the following is a point on the following function?
One way to approach this problem would be to plug in each answer and see what works. However, I would be a little more strategic and eliminate any options that don't make sense.
Our y value will never be negative, so eliminate any options with a negative y-value.
Try (0,0) really quick, since it's really easy
The only point that makes sense is (5,83), therefore it is the correct answer
One way to approach this problem would be to plug in each answer and see what works. However, I would be a little more strategic and eliminate any options that don't make sense.
Our y value will never be negative, so eliminate any options with a negative y-value.
Try (0,0) really quick, since it's really easy
The only point that makes sense is (5,83), therefore it is the correct answer
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Evaluate: 
Evaluate:
Cancel the absolute value sign by separating the function 
into its positive and negative counterparts.
Evaluate the first scenario.
Evaluate the second scenario.
The correct answer is:
Cancel the absolute value sign by separating the function
Evaluate the first scenario.
Evaluate the second scenario.
The correct answer is:
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If 
, then what is the value of 
when 
?
If 
We evaluate for 
Since the absolute value of any number represents its magnitude from 
and is therefore always positive, the final answer would be 
We evaluate for
Since the absolute value of any number represents its magnitude from 
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If 
is the greatest integer function, what is the value of 
?
If
The greatest integer function takes an input and produces the greatest integer less than the input. Thus, the output is always smaller than the input and is an integer itself. Since our input was 
, we are looking for an integer less than this, which must be 
since any smaller integer would by definition not be "greatest".
The greatest integer function takes an input and produces the greatest integer less than the input. Thus, the output is always smaller than the input and is an integer itself. Since our input was
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Let
What does 
equal when 
?
Let
What does
Because 3>0 we plug the x value into the bottom equation.
Because 3>0 we plug the x value into the bottom equation.
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Let
What does 
equal when 
?
Let
What does
Because 
we use the first equation.
Therefore, plugging in x=0 into the above equation we get the following,
.
Because
Therefore, plugging in x=0 into the above equation we get the following,
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Determine the value of 
if the function is
Determine the value of
In order to determine the value of 
of the function we set 
The value comes from the function in the first row of the piecewise function, and as such
In order to determine the value of
The value comes from the function in the first row of the piecewise function, and as such
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Determine the value of if the function is
Determine the value of
In order to determine the value of of the function we set
The value comes from the function in the first row of the piecewise function, and as such
In order to determine the value of
The value comes from the function in the first row of the piecewise function, and as such
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For the function 
defined below, what is the value of 
when 
?
For the function 
Evaluate the function for 
. Based on the domains of the three given expressions, you would use 
, since 
is greater than or equal to 
.
Evaluate the function for 
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