Question

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

Answer 1

Answer:

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

Step-by-step explanation:

Given a function:

$F(x) =-x+1$

To find:

Function $g$ 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:

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