question archive The "int()" operator in your calculator is the "greatest integer function
The "int()" operator in your calculator is the "greatest integer function
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The "int()" operator in your calculator is the "greatest integer function." It returns the greatest integer less than or equal to the operand and is written using square brackets: [x] or [[x]]. For example, it would give back 82 for [[82.976]]. In Smalltown, AZ the students receive grade points as follows:
4.0 for any grade 90% or higher. [90,100)
3.0 for any grade 80% or higher. [80,90)
2.0 for any grade 70% or higher. [70,80)
1.0 for any grade 60% or higher. [60,70)
(Notice: students NEVER fail! And students never get 100%!)
A. Write a function that correctly returns grade points for gradesfrom 60% to 100%. (78.45
should give a 2.0). Is your function even, odd, or neither?
B. State the domain and range of the function for this situation.
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Answer:
A) y(x) = ?[x/10?−5]? will give the grade point for the required percentage.
The function is neither even nor odd.
B) Domain of function x (60,100)
Range of function y {1,2,3,4}
Note:
For x> 0
[x] is less than equal to x
For example if x = 2.3
[2.3] = 2
For x <0
[x]= is less than equal to x
For example if x =-2.3
[-2.3] = -3
Thus, [x]+[-x]= -1
[x]-[-x] = 2[x] +1
Step-by-step explanation
A) Let a student gets x% marks such that x is between 60 to 100
?10x?? will give a number that will vary from 6 to 10
y(x) = ?[x/10?−5]? will give the grade point for the required percentage.
y(-x) = ?[−x/10?−5]?
Since, y(x) is not equal to y(-x). Neither y(x) =-y(-x)
The function is neither even nor odd.
B) Domain of function x (60,100)
Range of function y {1,2,3,4}
