What effect does replacing x with x−4 have on the graph for the function f(x)?
f(x) = ∣x−6∣+2
The graph is shifted 4 units up
The graph is shifted 4 units down.
The graph is shifted 4 units left.
The graph is shifted 4 units right.
To determine the effect of replacing x with x-4 on the graph of the function f(x) = |x-6| + 2, we can follow these steps:
1. Replace x with x-4 in the original function:
f(x-4) = |(x-4)-6| + 2
2. Simplify the expression:
f(x-4) = |x-10| + 2
Based on this, the effect of replacing x with x-4 is a horizontal shift of 4 units to the right.
To determine the effect of replacing x with x-4 on the graph of the function f(x) = |x-6| + 2, we need to substitute x-4 into the function and observe the resulting shift in the graph.
Substituting x-4 into f(x), we get:
f(x-4) = |(x-4)-6| + 2
Simplifying, we have:
f(x-4) = |x-10| + 2
Comparing this with the original function f(x) = |x-6| + 2, we can see that replacing x with x-4 has shifted the graph 4 units to the right. So the correct answer is:
The graph is shifted 4 units right.