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
To find the value of k, we need to determine the amount of shift that occurs when the graph of f(x) = 2x + 4 is replaced with f(x) = 2x − k.
Step 1: Start with the equation f(x) = 2x + 4. This represents a linear function.
Step 2: To shift a graph horizontally, we need to adjust the x-values. Since the graph shifts five units to the right, we subtract 5 from the original function.
Step 3: Rewrite the equation as f(x) = 2(x - 5) + 4.
Step 4: Simplify the equation: f(x) = 2x - 10 + 4.
Step 5: Combine like terms: f(x) = 2x - 6.
Step 6: Now compare the function f(x) = 2x - 6 to f(x) = 2x - k. The two functions are equivalent only if the coefficient of x and the constant term are the same.
Step 7: From the comparison, we can see that k is equal to -6.
Therefore, the value of k is -6.
To solve this problem, we need to understand the concept of shifting a graph. When a graph shifts to the right by a certain number of units, it means that we are adding that number to the x-values of the points on the graph.
In this case, we are given the equation of the original graph, f(x) = 2x + 4, and are told that it shifts five units to the right to become f(x) = 2x - k.
Let's analyze the effect of shifting on the equation. If we substitute x + 5 for x in the original equation, we should obtain the equation after the shift:
f(x + 5) = 2(x + 5) + 4
= 2x + 10 + 4
= 2x + 14
Comparing this equation to f(x) = 2x - k, we can see that they are equal when -k = 14. This means that k = -14.
However, we want to find the value of k, not -k. Therefore, the correct answer is k = 14.
So, the value of k is 14.
shifting f(x) to the right by 5 replaces x by (x-5), so you get
2(x-5)+4 = 2x-6
I suspect a typo. Get out some graph paper to check.