Question

If f(x) = x2 - 4x + 3, and the domain is (-2,0, 1}, what is the range?

Answer 1

Answer:

{15, 3, 0}

Step-by-step explanation:

• Domain = the set of all x-coordinates
• Range = the set of all y-coordinates

Plugin the domain values into the equation then solve:

(fx) = x²- 4x + 3

First value

y = -2²- 4(-2) + 3                      replace f(x) with y

y = 4 - (-8) + 3                         -2² = -2 times -2 = 4 and 4 times -2 = -8

y = 12 + 3                                 add

y = 15                                       final result; first range value

Second value

y = 0²- 4(0) + 3                      replace f(x) with y

y = 0 - 0 + 3                          0² = 0 times 0, which is 0 and 4 times 0 is 0

y = 0 + 3                                add

y =  3                                     final result; second range value

Third value

y = 1²- 4(1) + 3                       replace f(x) with y

y = 1 - 4 + 3                           1 times 1 is 1, 4 times 1 is 4

y = -3 + 3                               add

y = 0                                      final result; third (last) range value

Therefore, Range: {15, 3, 0}

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