Question

The graph of f(x) = 3.2x-3 is shown below. g(x) is a transformation of f(x).

How would you write the equation for the function g(x)?

Answer 1

C. g(x) = 3·2^x +2

Explanation:

The graph of g(x) appears to be a translation upward of the graph of f(x).

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To find the equation of g(x), we can add 5 to f(x), since the translation appears to be 5 units. (The y-intercept of f(x) is 0; the y-intercept of g(x) is 5.)

g(x) = f(x) +5

g(x) = (3·2^x -3) +5

g(x) = 3·2^x +2

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You can also determine the correct choice by looking at the value at x=0:

A. g(0) = 3 +6 = 9

B. g(0) = 1 +3 = 4

C. g(0) = 3 +2 = 5 . . . . matches g(0) on the given graph

D. g(0) = 3