Question

The tables below show the values of f(x) and g(x) for different values of x:

f(x) = 2(3)x

x f(x)
−2 0.22
−1 0.67
0 2
1 6
2 18

g(x) = 3x + 9

x g(x)
−2 9.11
−1 9.33
0 10
1 12
2 18

Based on the tables, what is the solution to the equation 2(3)x = 3x + 9? (1 point)


a. x = 0

b. x = 2

c. x = 12

d. x = 18

Answer 1

You are given two tables and asked to find the value of x such that f(x) is equal to g(x). One table lists values for f(x); the other lists values for g(x). You are essentially being asked to find the line in one table that matches a line in the other table. When you compare line-by-line, you find that the lines that match are

(x, f(x)) = (2, 18) and (x, g(x)) = (2, 18)

This tells you ...

f(2) = 18 = g(2) . . . . that is, f(x) = g(x) when x=2

Comparing to the offered answer choices, you must conclude the solution is ...

b. x = 2