Questions: This question has two parts. First, answer Part A. Then, answer Part B. Part A a. Determine the value of k from the given graph. f(x)=3^x ; g(x)=f(x)+k The value of k is □

This question has two parts. First, answer Part A. Then, answer Part B. Part A
a. Determine the value of k from the given graph.
f(x)=3^x ; g(x)=f(x)+k

The value of k is □

Transcript text: This question has two parts. First, answer Part A. Then, answer Part B. Part A a. Determine the value of $k$ from the given graph. \[ f(x)=3^{x} ; g(x)=f(x)+k \] The value of $k$ is $\square$

Solution

Solution Steps

Step 1: Analyze the graph

The graph of g(x) appears to be a vertical translation of the graph of f(x) = 3^x. The base function f(x) = 3^x would pass through the point (0,1). The graph of g(x) passes through the point (0,2).

Step 2: Determine the vertical shift

The graph of g(x) is shifted one unit up from the graph of f(x). This indicates a vertical translation of +1.

Step 3: Determine the value of k

Since g(x) = f(x) + k and the vertical shift is +1, the value of k is 1.