Question

using the graph, choose the correct formula for the function g
a ( g(x) = f(x) + 1 )
b ( g(x) = f(x) - 3 )
c ( g(x) = f(x + 1) )
d ( g(x) = f(x - 3) )

Explanation:

Step1: Analyze Vertical Shift

Check the vertical position of \( g(x) \) relative to \( f(x) \). If \( g(x) \) is above \( f(x) \) by a constant, it's a vertical shift. From the graph, \( g(x) \) is shifted up by 1 unit. So the transformation is \( g(x)=f(x)+1 \), which matches option A.

Step2: Eliminate Other Options

• Option B: \( g(x)=f(x)-3 \) would shift down, not up. Eliminate.
• Option C: \( g(x)=f(x + 1) \) is a horizontal shift left, not vertical. Eliminate.
• Option D: \( g(x)=f(x - 3) \) is a horizontal shift right, not vertical. Eliminate.

Answer:

A. \( g(x) = f(x) + 1 \)