Question

The graph of f(x) = 2x + 3 shifts 10 units to the right when it is replaced with the graph of f(x) = 2x − k. What is the value of k?

Answer 1

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.

Answer 2

`k = 17`

Step-by-step explanation

The given function is

`f(x) = 2x + 3`

The translation that shifts this function 10 units to the right is

`f(x - 10)`

This implies that

`f(x - 10) = 2(x - 10) + 3`

We expand the parenthesis to get:

`f(x - 10) = 2x -20+ 3`

`f(x - 10) = 2x - 17`

Comparing this equation with

`f(x) = 2x - k`

we have

`k = 17`