The only increasing function is the last option:
[tex]f(x) = 5^x[/tex]
Which function is increasing?
Here we only need to see that, is as x increases also do f(x). Then the function will be increasing.
The cases for exponential functions is actually more trivial than that.
- If the base is between zero and 1, then the function is decreasing.
- If the base is larger than 1, then the function is increasing.
In the given options there is only one function with a base larger than 1, which is the last option:
[tex]f(x) = 5^x[/tex]
That is the correct option.
If you want to learn more about exponential functions:
https://brainly.com/question/11464095
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