Question

Write a rule for g described by the transformation of the graph of f...

Answer 1

`g(x) = 4-4√(x)`

Explanation:

Given

`f(x) = 4√(x)+1`

1. 5 units down translation

2. Reflection in the x-axis

Required

Determine the resulting function g

1. 5 units down translation

This is defined by the rule:

A down translation is:

`f'(x) = f(x) - b`

Where b is the number of units.

So, we have:

`f'(x) = 4√(x) + 1 - 5`

`f'(x) = 4√(x) -4`

2. Reflection in the x-axis

For a function f(x),

When reflected over the x-axis, it becomes -f(x)

So:

`g(x) = -f(x)`

`g(x) = -(4√(x) - 4)`

`g(x) = -4√(x) +4`

`g(x) = 4-4√(x)`