Respuesta :

jacob193

Answer:

The second choice, [tex](-1,\, 12)[/tex].

Step-by-step explanation:

Note, that the expression [tex]y = f(x)[/tex] is an equation. A point [tex](x,\, y)[/tex] is on the graph of [tex]y = f(x)\![/tex] if and only if the value of [tex]x[/tex] and [tex]y[/tex] satisfy this equation; that is: in other words, the [tex]y\![/tex]-coordinate of that point (the second number in the tuple) should be equal to [tex]f(x)[/tex], which is equal to [tex](-3\, x +9)[/tex] (evaluated where [tex]x\![/tex] is equal to the first number in the tuple.

For each tuple in the choices, calculate the value of [tex]f(x)[/tex] where [tex]x[/tex] is equal to the first number of each tuple. Compare the result to the second number in that tuple. That choice corresponds to a valid point on [tex]y = f(x)[/tex] only if these two numbers match.

  • First choice: [tex]x = 1[/tex], [tex]f(x) = f(1) = -3 + 9 = 6[/tex]. That's not the same as the second number, [tex]-10[/tex]. Therefore, this point isn't on the graph of [tex]y = f(x)[/tex].
  • Second choice: [tex]x = -1[/tex], [tex]f(x) = f(-1) = (-3)\times (-1) + 9 = 3 + 9 = 12[/tex]. That matches the second number in the tuple. Therefore, this point is on the graph of [tex]y = f(x)[/tex].
  • Third choice: [tex]x = 2[/tex], [tex]f(x) = f(2) = (-3)\times 2 + 9 = 3[/tex]. That's not the same as the second number, [tex](-3)[/tex]. Therefore, this point isn't on the graph of [tex]y = f(x)[/tex].
  • Fourth choice: [tex]x = -2[/tex], [tex]f(x) = f(-2) = (-3)\times (-2) + 9 = 15[/tex]. That's not the same as the second number, [tex]13[/tex]. Therefore, this point isn't on the graph of [tex]y = f(x)[/tex].