Question

if the graph of ( f(x) ) is:
which of the following is the graph of ( f(x - 1) )?
a.
b.
c.

Explanation:

Step1: Recall Horizontal Shift Rule

For a function \( y = f(x - h) \), the graph of \( f(x) \) is shifted horizontally by \( h \) units. If \( h>0 \), it's a shift to the right; if \( h<0 \), it's a shift to the left. Here, \( h = 1 \), so we shift the graph of \( f(x) \) 1 unit to the right.

Step2: Analyze Original and Shifted Graph

The original graph of \( f(x) \) has its peak (or the vertex of the piece - wise linear graph) at \( x = 0 \) (assuming the original graph is symmetric around or has its key point at \( x = 0 \) initially). After shifting 1 unit to the right, the key point (the vertex of the triangular - like graph) should move from \( x = 0 \) to \( x=0 + 1=1 \).

Looking at the options:

• Option A: The graph seems to be shifted left, which would correspond to \( f(x + 1) \), not \( f(x - 1) \).
• Option B: The graph has its key point (the vertex of the small triangle) at \( x = 1 \), which is a shift of the original graph 1 unit to the right, matching the transformation \( f(x-1) \).
• Option C: The graph seems to be shifted down or has a different vertical/horizontal shift that does not match the horizontal shift of 1 unit to the right.

Answer:

B. The graph with the triangular part having its vertex at \( x = 1 \) (the second option labeled as B)