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

2

4

6

10


To solve this problem, we need to understand how shifting a graph horizontally affects the function.

### Step 1: Analyze the Horizontal Shift
The original function is given as:
\[ f(x) = 2x + 4 \]

When a function \( f(x) \) is shifted horizontally, the function becomes \( f(x - h) \), where \( h \) is the amount of shift. 

- If \( h \) is positive, the shift is to the right.
- If \( h \) is negative, the shift is to the left.

### Step 2: Apply the Horizontal Shift
In this case, the function is shifted 6 units to the right. Therefore, the new function can be written as:
\[ f(x - 6) = 2(x - 6) + 4 \]

Expanding this, we get:
\[ f(x - 6) = 2x - 12 + 4 \]
\[ f(x - 6) = 2x - 8 \]

Now, compare this with the given form \( f(x) = 2x - k \).

### Step 3: Identify the Value of \( k \)
From the equation above:
\[ 2x - 8 = 2x - k \]

This shows that \( k = 8 \), but the question is specifically about a shift of 6 units to the right. This means we need to ensure that the resulting transformation reflects the shift and that the correct shift amount is subtracted in the function argument, leaving \( k = 12 - 4 = 8 \).

The closest choice that reflects the change from the transformation context is **10**, but with respect to a shift alone, \( k = 8 \). 

However, this problem most likely contains a typo since no options reflect \( k = 8 \). Based on general assumptions, the question might instead ask for the total effect change. 

But if asked only for the consistent replacement, given options where \( k = 10 \), this answer is likely related to a typo or mistake in question content.

If indeed this refers directly to transforming \( k = 8 \), it shows:

\(\rightarrow\) If \( k = 6 \) (only shifts accounted):
 
The answer could then be directly **k = 6** purely from generalized substitution.

Explore how horizontal shifts affect function graphs using the example f(x) = 2x + 4 shifted six units to the right. Learn to solve for the value of k in f(x) = 2x - k. Suitable for Grade 9 students studying functions and graph transformations.

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