Question

The parenthesis are been used just as the absolute value signs. * 2 points Given the parent function f(x) = r, the function g(x) = (x - 1)3 - 2 is the result of a shift of f(x) (1) 1 unit left and 2 units down (2) 1 unit left and 2 units up (3) 1 unit right and 2 units down (4) 1 unit right and 2 units up 0 1 2 3 O 4

Answer 1

Graph and equations

We know that every equation expressed in terms of x can be graph in an x-y plane, in this case the equation is

`f(x)=x^3`

if we want to move it up or down we add or substract the quantity of unities we are moving it. If we want to move it down two unities we substract 2 on the whole equation:

`x^3\Rightarrow x^3-2`

If we want to move it to the left or to the right we add or substract the quantity of unities we are moving it to the x term. If we add it means it is going to the left and if we substract it means it is going to the right. If we want to move it one unity to the right then we substract 1 from the x :

`x^3\Rightarrow x^3-2\Rightarrow(x-1)^3-2`

Then, the function:

`g(x)=(x-1)^3-2`

is the result of moving

f(x) = x³

1 unit to the right and 2 units down

Answer: 3