Question

The graph of g(x) is the graph of f(x)=x−2 reflected across the y-axis. Which equation describes function g?

Answer 1

Answer:

y = -x -2

Step-by-step explanation:

In order to transform the graph of a function to give a reflection across the y-axis, the variable "x" of its expression needs to be multiplied by (-1).

Therefore in our case, starting with f(x) = x - 2 , the transformed function g(x) should read: g(x) = -x -2

Answer 2

Answer:

$g(x) = -x + 2$

Step-by-step explanation:

We are given the following information:

$f(x)=x-2$

We describe g(x) as a reflection over y-axis of f(x).

We have to find the equation of g(x).

Reflection over y-axis can be written as:

$y = x-2\\-y = -x + 2$

Thus, the image of g(x) is of the form -y and  g(x) will have equation of the form:

$g(x) = -x + 2$

In the graph, the blue line represents the function f(x) and g(x) is represented by green line.

The graph for both the functions is shown in the image