Question

1

Select the correct answer from each drop-down menu.
The function () = 13 has been transformed, resulting in function h.
h(t) = -(1 + 2)2 – 4
To create function h, function fwas translated 2 units
„. translated 4 units
and reflected across the

Answer 1

To create function h, function f was translated 2 units right , translated 4 units up and reflected across the x axis

Explanation:

Given

`f(x) = x^3`

`h(x) =-(x + 2)^3 - 4`

Required

Complete chart

First: f(x) was translated right by 2 units

The rule of right translation is
`(x,y) \to (x + 2,y)`

So, we have:

`f'(x) = f(x + 2)`

`f'(x) = (x + 2)^3`

Next: f'(x) was translated up by 4 units

The rule of down translation is
`(x,y) \to (x,y+4)`

So, we have:

`f`

`f`

Lastly, f"(x) was reflected across the x-axis;

The rule of this reflection is:
`(x,y) \to (x,-y)`

So, we have:

`h(x) = -f`

`h(x) = -[(x+2)^3 + 4]`

Remove bracket

`h(x) = -(x+2)^3 - 4`