Question

identify function transformations
g is a transformation of f. the graph below shows f as a solid blue line and
g as a dotted red line.
what is the formula of g in terms of f?
choose 1 answer:
a ( f(x - 2) )
b ( f(x + 2) )
c ( f(x) - 2 )
d ( f(x) + 2 )

Explanation:

Step1: Analyze horizontal shift

To determine the transformation from \( f(x) \) to \( g(x) \), we check the horizontal shift. A horizontal shift of \( h \) units is given by \( f(x - h) \) (right shift) or \( f(x + h) \) (left shift).
Looking at the graphs, the vertex (or key point) of \( g(x) \) is shifted 2 units to the left compared to \( f(x) \).

Step2: Determine the transformation formula

A left shift by 2 units means replacing \( x \) with \( x + 2 \) in the function. So the formula for \( g(x) \) is \( f(x + 2) \).

Answer:

B. \( f(x + 2) \)