Question

If f (x) = –2x – 3 and the domain of f is {-4,0,6} , what is the range of
f (x)?

Answer 1

`\lbrace 5,\, -3,\, -15 \rbrace`.

Explanation:

The domain of a function includes all the values that this function could accept as inputs. The function would give a (possibly non-unique) output for each of these inputs. The range of this function over this particular domain would be the set of all the possible output values from this function.

In this question, the domain of this function is
`\lbrace -4,\, 0,\, 6 \rbrace`, meaning that this function could accept
`x = (-4)`,
`x = 0`, and
`x = 6` as possible inputs.

• 
  `f(-4) = -2 * (-4) - 3 = 8 - 3 = 5`.
• 
  `f(0) = -3`.
• 
  `f(6) = -2 * 6 - 3 = -15`.

In other words, the possible output values of this function over this domain are
`5`,
`(-3)`, and
`(-15)`. Hence, the range of this function would be the set
`\lbrace 5,\, -3,\, -15 \rbrace`.