ANSWER
[tex]k = 17[/tex]
EXPLANATION
The given function is
[tex]f(x) = 2x + 3[/tex]
The translation that shifts this function 10 units to the right is
[tex]f(x - 10)[/tex]
This implies that
[tex]f(x - 10) = 2(x - 10) + 3[/tex]
We expand the parenthesis to get:
[tex]f(x - 10) = 2x -20+ 3[/tex]
[tex]f(x - 10) = 2x - 17[/tex]
Comparing this equation with
[tex]f(x) = 2x - k[/tex]
we have
[tex]k = 17[/tex]
k=17
The new function would be f(x)=2x-17
In the previous function when u put x=0 you got 3.
Now when the function moves 10 units to the right you still have to get y=3 for x=10. So
2x-k=3 substitute 10 for x
20-k=3 solve for k
K=17.
