Question

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

k = 6

Explanation:

Let consider a function in the form:

f(x) = ax + b

A horizontal shift "z" units to the right would be:

f(x) = a(x-z) + b

and

A horizontal shift "z" units to the left would be:

f(x) = a(x+z) + b

So, in this function, it will shift horizontally 5 units right, so it will become:

f(x) = 2(x-5) + 4

Simplifying, it will become:

`f(x) = 2(x-5) + 4\\f(x)=2x-10+4\\f(x)=2x-6`

If it is replaced with "f(x) = 2x - k"

Matching, we can see that k = 6

Thus,

k = 6

(answer choices provided are wrong or question is wrong, but i did as the question, thanks)