Transformations are used to change the position of a function from one point to another. When f(x) is reflected over the y-axis, the new function g is [tex]g(x) = x + 8[/tex]
Given that:
[tex]f(x) = -3+|x - 11|[/tex]
To reflect across the y-axis, we use the following transformation rule:
[tex](x,y) \to (-x,y)[/tex]
So, the new function is:
[tex]g(x) = f(-x)[/tex]
If [tex]f(x) = -3+|x - 11|[/tex], then:
[tex]f(-x) = -3+|-x - 11|[/tex]
Factor out -1
[tex]f(-x) = -3+|-1(x + 11)|[/tex]
Remove absolute sign
[tex]f(-x) = -3+1 \times (x + 11)[/tex]
[tex]f(-x) = -3+x + 11[/tex]
Collect like terms
[tex]f(-x) = x + 11-3[/tex]
[tex]f(-x) = x + 8[/tex]
Hence, the new function is:
[tex]g(x) = x + 8[/tex]
Read more about transformations at:
https://brainly.com/question/12865301
