Question

Help please! The graph of f(x) = 2x + 4 shifts five units to the right when it is replaced with the graph of f(x) = 2x − k. What is the value of k? 5 −1 1 4

Answer 1

To shift to the right you need to make it MINUS the amount of units

f(x) = 2x + 4

to shift 5 to right

f(x) = 2x + 4 - 5

f(x) = 2x - 1

Since the equation is f(x) = 2x - k

We already have the minus in the k, so k isnt equal to -1, its equal to 1.

Alternative 1.

Answer 2

k is equal to 1

Explanation:

Since this is a geometric transformation called, translation, therefore the shifted function f'(x) is parallel to f(x), then the slope m=2 remains the same for f'(x). So f'(x)=2x -k. The shifting is five units to the right then, we have to subtract -5 to f(x)=2x+4, so:

`f'(x)=2x-k\Rightarrow f'(x)=2x+(4-5)\Rightarrow f'(x)=2x-1`

Proving the 5 units shifting

f(x)=2x+4

x| y

1 | 6

2|8

f'(x)=2x-1

x|y

1| 1

2|3

Notice that every number ∈ to the Range of f(x) has a difference of 5 units when compared to f'(x) Range values.

6-1=5

8-3=5