SOLUTION: For the function f(x)= -(x^2-x), where x is an integer, the range can be defined as: A. y is less than or equal to 0 B. y is greater than or equal to 0 C. y is less than 0 D.

Question 629281: For the function f(x)= -(x^2-x), where x is an integer, the range can be defined as:
A. y is less than or equal to 0
B. y is greater than or equal to 0
C. y is less than 0
D. y is less than -2
E. y is less than or equal to -2
Found 2 solutions by vleith, stanbon:
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
A.
The domain is all values of integer x . You know that x^2 >= x for all integer x. At 0, x^2 = x, for all other values of integer x, x^2 > x.
Since the function includes a negative, then the largest value f(x) can be is 0. All other values are less than 0.
So, the answer is A
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
For the function f(x)= -(x^2-x), where x is an integer, the range can be defined as:
A. y is less than or equal to 0
B. y is greater than or equal to 0
C. y is less than 0
D. y is less than -2
E. y is less than or equal to -2
-----------------------
y = -x^2+x
y = -x(x-1)
-----
x-intercepts are 0 and 1
Parabola opens down
Max occurs at x = -b/(2a) = -1/(2*-1) = 1/2
Max value = f(1/2) = (-1/2)((1/2)-1) = -1/2*(-1/2) = 1/4
---
Range is "All Real Numbers less than of equal to 1/4.
=============================================================
Note: None of your "option answers" is correct for the
problem you posted.
==========================
Cheers,
Stan H.
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