When a function is shrunk vertically, the function has undergone a form of transformation.
The resulting function when [tex]f(x) = 2x + 6[/tex] vertically shrink by 1/2 is [tex]f'(x) = x + 3[/tex]
Given that:
[tex]f(x) = 2x + 6[/tex]
[tex]k = \frac 12[/tex] --- shrink factor
When a function is shrunk vertically, the rule of transformation is:
[tex](x,y) \to (x,ky)[/tex]
So, we have:
[tex]f'(x) = k f(x)[/tex]
The new function becomes
[tex]f'(x) = \frac 12 \times (2x + 6)[/tex]
[tex]f'(x) = x + 3[/tex]
Hence, when [tex]f(x) = 2x + 6[/tex] is vertically shrunk by 1/2, the new function is [tex]f'(x) = x + 3[/tex]
Read more about transformations at:
https://brainly.com/question/11709244
