Write a function g whose graph represents a reflection in the y-axis of the graph F(x)=-x+1

Question

asked Nov 13, 2021 216k views

1 Answer

Elva · Answer 1 · 2021-11-17T02:00:12+0000

Answer:

$\bold{g(x) = x+1}$

Explanation:

Given a function:

F(x) =-x+1

To find:

Function
whose graph is a reflection in the y -axis for the given function = ?

Solution:

First of all, let us learn about the reflection of a point (
x, y ) in y axis.

For example, let us consider a point (3, 2) on the coordinate axis.

The reflection of this point in y axis will be (-3, 2)

OR

In other words, To find the image of a point in y axis:

the x coordinate is made of negative sign and y coordinate remains the same.

A line is nothing but a number of points joined together.

So, if we want to find reflection of a line or linear function in y axis, we just make the sign of x as negative.

Given that
F(x) =-x+1

We can write it as:

F(x)=y =-x+1

To find its reflection:

$g(x) = - (-x)+1\\\Rightarrow \bold{g(x) = x+1}$

Please refer to the attached graphs of
F(x) and
g(x) .

So, the answer is:

$\bold{g(x) = x+1}$