Final answer:
The function g(x)=3×2^x+5 represents a horizontal translation of the original function f(x)=2 by 5 units to the left, which is answer choice (b) – 5.
Step-by-step explanation:
When looking at the exponential function f(x) = 2 and its transformation to g(x) = 3×2x+5, we can analyze the horizontal translation that has occurred. According to algebraic principles, a function of the form f(x – d) is translated d units to the right. Hence, if we had a function f(x + d), it would imply a translation of d units to the left.
Observing the transformation to g(x), we can rewrite it to see if it fits either form. Since there's no subtraction by a value inside the function, i.e., it's not in the form of f(x – d), we can conclude that there is no translation to the right. However, if we were to rewrite g(x) into the form f(x + d), by factorizing the exponent, this would become g(x) = 3×2(x + log2(25)) or g(x) = 3×2x + 5, implying that the function f(x) has been translated 5 units to the left, which corresponds to choice (b).
Therefore, the correct answer is (b) – 5, indicating a horizontal translation of 5 units to the left in the transformation from f(x) to g(x).