Question

Write a function h(x) that shows a transformation of f(x) left 3 units & reflects it over the x axis

Answer 1

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

Explanation:

Given

`f(x) = x^2` --- the parent function

Required

Determine h(x)

First, translate f(x) 3 units left

The rule is:

`(x,y) \to (x - 3, y)`

So, we have:

`f(x) = x^2`

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

Next, reflect over x-axis

The rule is:

`(x,y) \to (x,-y)`

So, we have:

`h(x) = -f(x)`

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