Question

Let f(x)=3^x, Let g(x) = 3^x−2+5. Which two statements describe the graph of g(x) with respect to the graph of f(x)? 1) A. g(x) is translated 2 units right from f(x). 2) B. g(x) is translated 2 units left from f(x). 3) C. g(x) is translated 5 units down from f(x). 4) D. g(x) is translated 5 units up from f(x).

Answer 1

The graph of g(x) = 3^x−2+5 is translated 2 units to the right and 5 units up from the graph of f(x)=3^x.

Step-by-step explanation:

In relation to the function f(x)=3^x, the function g(x) = 3^x−2+5 demonstrates a change in the form of a translation. According to the principles of function translation, the term -2 in the exponent of g(x) shifts the graph 2 units to the right. Therefore, the first statement, A. g(x) is translated 2 units right from f(x), correctly describes the transformation. Additionally, the +5 at the end of g(x) vertically shifts the graph upward by 5 units. Hence, the fourth statement, D. g(x) is translated 5 units up from f(x), accurately represents the transformation.

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