Question

Write a function g whose graph represents the indicated transformation of the graph of F. Let g be a translation 4 units down and a horizontal shrink by a factor of of the graph of f(x) = x.​

Answer 1

g(x) = 6x+4

Explanation:

The given function f(x)=x

Let p(x) be an intermediate function after translation of f(x).

So, after the translation 4 unit down, the new function

p(x) = f(x) - 4

p(x) = x-4

Now, there is a horizontal shrink by a factor of 6, so the required function g(x) is

g(x) = p(6x) [here 6 is the horizontal shrink factor]

g(x) = 6x-4

Hence, the required function is g(x) = 6x+4