Answer:
[tex]f'(x) = 2x - 10[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 2x + 4[/tex]
Required
Translate 7 units left
When a function f(x) is translated b units to the left, the resulting function is:
[tex]f'(x) = f(x-b)[/tex]
In this case:
[tex]f(x) = 2x + 4[/tex]
[tex]b = 7[/tex]
[tex]f'(x) = f(x-b)[/tex] becomes
[tex]f'(x) = f(x - 7)[/tex]
Calculating [tex]f(x-7)[/tex]
[tex]f(x-7) = 2(x-7)+4[/tex]
[tex]f(x-7) = 2x-14+4[/tex]
[tex]f(x-7) = 2x-10[/tex]
So:
[tex]f'(x) = 2x - 10[/tex]
