Answer:
a) Translate the graph of f(x) down 3 units.
b) (8,-1) is a point on the graph of g(x)
Step-by-step explanation:
The transformations that subtract a constant number of units from the functional expression f(x) are transformations that lower the graph of the function in those many units,
Therefore they correspond to a translation of the original graph down the number of units involved.
In this case, the number of units involved is "3" (due to the "-3" added to the expression for f(x). So he correct answer for the first part is: Translate the graph of f(x) down 3 units.
For the second part, one has to try each of the coordinate pairs given in the new function g(x) to see which one results in a true statement:
1) Testing (-8,-1) by checking if replacing x with the value "-8" renders "-1" for the y-value: [tex]g(x)=\sqrt[3]{x} -3\\g(-8)=\sqrt[3]{-8} -3\\g(-8)=-2-3\\g(-8)=-5[/tex]
so this is NOT a point on the graph of g(x).
2) Testing (-1,-2) by checking if replacing x with the value "-1" renders "-2" for the y-value: [tex]g(x)=\sqrt[3]{x} -3\\g(-1)=\sqrt[3]{-1} -3\\g(-1)=-1-3\\g(-1)=-4[/tex]
so this is NOT a point on the graph of g(x).
3) Testing (2,-1) by checking if replacing x with the value "2" renders "-1" for the y-value: [tex]g(x)=\sqrt[3]{x} -3\\g(2)=\sqrt[3]{2} -3\\[/tex]
the cubic root of 2 is not a rational number, because 2 is not a perfect cube, so the expression cannot be reduced, so this is NOT a point on the graph of g(x).
4) Testing (8,-1) by checking if replacing x with the value "8" renders "-1" for the y-value: [tex]g(x)=\sqrt[3]{x} -3\\g(8)=\sqrt[3]{8} -3\\g(8)=2-3\\g(8)=-1[/tex]
Therefore this pair (8,-1) IS a point on the graph of g(x).
