Question

the function g(x) is a transformation of the parent function f(x). decide how f(x) was transformed to make g(x).

f(x) table:

x	y
-2	1/9
-1	1/3
2	9
3	27
4	81

g(x) table:

x	y
-2	1/81
-1	1/27
2	1
3	3
4	9

options:
a. horizontal or vertical reflection
b. horizontal or vertical stretch
c. reflection across the line y = x
d. horizontal or vertical shift

Explanation:

Step1: Analyze function values

Compare \( f(x) \) and \( g(x) \) values. For \( x = -2 \), \( f(-2)=\frac{1}{9} \), \( g(-2)=\frac{1}{81}=\frac{1}{9^2} \); \( x = -1 \), \( f(-1)=\frac{1}{3} \), \( g(-1)=\frac{1}{27}=\frac{1}{3^3} \); \( x = 2 \), \( f(2)=9 \), \( g(2)=1=\frac{9}{9} \); \( x = 3 \), \( f(3)=27 \), \( g(3)=3=\frac{27}{9} \); \( x = 4 \), \( f(4)=81 \), \( g(4)=9=\frac{81}{9} \).

Step2: Identify transformation type

Notice \( g(x)=\frac{f(x)}{9} \) (vertical compression) or \( g(x)=f(x - a) \)? No, values are scaled. Vertical stretch/compression: \( g(x)=kf(x) \), here \( k=\frac{1}{9} \) (compression, a type of stretch). Reflection? No, signs same. Shift? No, values scaled, not shifted. So it's a vertical stretch (compression is inverse stretch). Option B is about stretch.

Answer:

B. Horizontal or vertical stretch