Question

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

Answer 1

Answer:

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

Step-by-step 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:

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

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