Which of the following is the function representing the graph below?

Question

graph begins in the second quadrant near the line y equals 1 and increases slowly while crossing the ordered pair 0, 2. When the graph enters the first quadrant, it begins to increase quickly throughout the graph.

 

Choose one answer.

 

A. f(x) = one-third to the power of x + 1

 

B. f(x) = one-third to the power of x - 1

 

C. f(x) = 3x - 1

 

D. f(x) = 3x + 1

Answer 1

Hello May,

 

I'd normally say that, without the graph, you're out of luck. But a valuable clue is that the graph goes through (0, 2).

 

 

The answer, then, is A but ONLY if you parse A as "f(x) = (1/3)^x + 1." Then at x = 0, you have f(0) = (1/3)⁰ + 1 = 2, and the graph goes through (0, 2).

I originally parsed this as "f(x) = (1/3)^x+1, and B similarly, in which case none of the answers works.

 

Given the description, however, none of the answers fits anyway, as the graph of A "begins" in the second quadrant at very high values of y, nowhere near y = 1. For example, at x = -6, f(x) = 3⁶ + 1 = 730. It passes through (0, 2) while leveling off the whole time, asymptotically approaching y = 1 as x approaches infinity.

 

Gee whiz...be careful!

 

Eric M.

McMinnville OR