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 Vertical Shift Rule

The transformation \( y = f(x) - k \) (where \( k>0 \)) shifts the graph of \( f(x) \) downward by \( k \) units. Here, \( k = 1 \), so we need to shift the graph of \( f(x) \) down by 1 unit.

Step2: Analyze Original Graph

The original graph of \( f(x) \) has a vertex (the peak) above the \( x \)-axis (since it starts at the origin and goes up then down). When we shift it down by 1 unit, every point \((x, y)\) on \( f(x) \) becomes \((x, y - 1)\) on \( f(x)-1 \).

Step3: Evaluate Options

• Option A: The graph is shifted horizontally and maybe vertically in a way that doesn't match a downward shift of 1. It looks like a horizontal shift or a different transformation.
• Option B: The graph is shifted up (since the starting point is higher on the \( y \)-axis), which is the opposite of what we need.
• Option C: The graph of \( f(x) \) shifted down by 1 unit. The original graph's vertex (and all points) are moved down by 1, so the "peak" and the starting point (origin) would move to \( y=-1 \) or adjusted down, matching the vertical shift down by 1.

Answer:

C. (The graph corresponding to option C, which shows the original graph of \( f(x) \) shifted downward by 1 unit)