Question

1

Answer 1

Answer:

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

Step-by-step 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:

$f"(x) = f'(x) +4$

$f"(x) = (x + 2)^3 +4$

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

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

So, we have:

$h(x) = -f"(x)$

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

Remove bracket

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