Question

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

Answer 1

Answer:

$g(x) = 4-4\sqrt{x}$

Step-by-step explanation:

Given

$f(x) = 4\sqrt{x}+1$

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:

$f'(x) = 4\sqrt{x} + 1 - 5$

$f'(x) = 4\sqrt{x} -4$

2. Reflection in the x-axis

For a function f(x),

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

So:

$g(x) = -f(x)$

$g(x) = -(4\sqrt{x} - 4)$

$g(x) = -4\sqrt{x} +4$

$g(x) = 4-4\sqrt{x}$