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  {-12, -8, 0, 8}

Step-by-step explanation:

The range is the set of y-values that correspond to the given set of x-values. I like to figure them "all at once", since the math is repetitive.

  f(x) = -2x +6

  f({-1, 3, 7, 9}) = -2{-1, 3, 7, 9} +6 = {2, -6, -14, -18} +6

  f({-1, 3, 7, 9}) = {8, 0, -8, -12}

The range for the given domain is {-12, -8, 0, 8}.

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.