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?

A.) -5
B.) -1
C.) 1
D.) 5

Answer 1

Option C. is the correct answer:

The value of k is 1

Explanation:

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Answer 2

C.) 1

Explanation

Remember the rules for shifting functions:

`f(x)+b` shifts the function b units upward

`f(x)-b` shifts the function b units downward

`f(x+b)` shifts the function b units to the left

`f(x-b)` shifts the function b units to the right

Since we want tho shift
`f(x)=2^(x+4)` 5 units to the right, we are using the rule:
`f(x-b)` shifts the function b units to the right; in other words, we need to subtract 5 units to the input of the function:

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

`f(x)=2^(x-1)`

But notice that there is already a negative sign in
`f(x)=2^(x-k)`, so to get
`f(x)=2^(x-1)`, k must be equal to positive 1.