Question

The graph of f(x) -3 -2 -3 is shown below. g(x) is a transformation of f(x).How would you write the equation for the function g(x)?005 10 15 20 25f) 3.2A. g(x) = 3.2 +2B. g(x) = 2* +3C. g(x) = 3.2*D. g(x)= 3.2+6

Answer 1

`g(x)=3\cdot2^x+2`

Step-by-step explanation

We want to write the equation for the function g(x).

From the graph, we see that g(x) was moved 5 units upward from the parent function, f(x). In other words, f(x) was translated vertically upward to result in g(x).

When an exponential function is translated vertically, it changes as follows:

`g(x)=f(x)+b`

when b > 0, it is an upward translation

when b < 0, it is a downward translation

Therefore, the equation for the function g(x) can be written as:

`\begin{gathered} g(x)=3\cdot2^x-3+5^{} \\ \Rightarrow g(x)=3\cdot2^x+2 \end{gathered}`