Shown below
Explanation:
The options aren't provided. However, we can answer this question. Here we have two exponential functions:
[tex]g(x)=3^x \\ \\ h(x)=2^{-x}[/tex]
- The function g(x) is an exponential growth.
- The function h(x) is an exponential decay.
So we are asked to find another function k(x):
[tex]k(x)=g(x)-h(x)[/tex]
In this new function we subtract h(x) from g(x), so:
[tex]k(x)=3^x-2^{-x}[/tex]
By using graphing tool, we get the graph as shown below. Notice that this graph passes through the origin because:
[tex]k(0)=3^0-2^{-0} \\ \\ k(0)=1-1 \\ \\ k(0)=0[/tex]
Learn more:
Making tables from functions: https://brainly.com/question/2142560
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