Question

Write a function g whose graph represents the indicated transformation of the graph of f​

Answer 1

Using translation concepts, the function for g(x) is given by:

g(x) = 4 - |x - 2|

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, the parent function is given by:

f(x) = 4 - |x + 1|.

Function g(x) is is a shift right of 3 units of f(x), hence:

g(x) = f(x - 3) = 4 - |x - 3 + 1| = 4 - |x - 2|.

More can be learned about translation concepts at brainly.com/question/4521517

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Answer 2

Step-by-step explanation:

the picture clearly indicates that g(x) is f(x) translated 3 units to the right.

that means that the functional value of g at x delivers the functional value of f at x-3 (3 units earlier).

so,

g(x) = f(x - 3) = 4 - |x - 3 + 1| = 4 - |x - 2|