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

Answer

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.

Answer 2

Answer:

Option C. is the correct answer:

The value of k is 1

Step-by-step explanation:

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