The graph of y=6-[sqrt(4-3x)] contains which point? a. (1,4) b.(0,1) c.(0,6) d. (1,5) e. (2,4) f. none of the above

Given y=6-[sqrt(4-3x)], focus on the sqrt function:  sqrt(4-3x).  Since the input of this function cannot be negative, any x-value used must pass the test 4-3x>0.  This is equivalent to 4>3x, or 3x<4, or x < 4/3.  This eliminates choice E.

Second, if the y value is an integer, then sqrt(4-3x) must be an integer.  

Checking answers A through D:  

A:  sqrt(4-3) = sqrt(1) = 1 (OK)        Then y=6-[sqrt(1)] = 5  (NO)

B:  sqrt(4-0) = 2 (OK)                     Then y=6-2 = 4   (NO)

C:  sqrt(4-0) = 2 (OK)                      Then y=6-2 = 4 (NO)

D:  sqrt(4-15) Not OK; eliminate

Correct  F:  None of the above answers are correct

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