Online Course Discussion Forum

A Question on a Function

 
 
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A Question on a Function
by Tina Jin - Saturday, 17 June 2023, 8:03 PM
 
Hello!


Why is the function f(x)=(3^(x))+x a strictly increasing function (or only one value of x corresponds to one value of f(x))? How can you tell directly without the graph? Even if there is a graph, how do you know what it looks like?


Thanks!


 
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Re: A Question on a Function
by Dr. Kevin Wang - Sunday, 18 June 2023, 12:17 AM
 

Good questions!  At the high school level, we don't need to get into the depth of why the function $3^x$ is strictly increasing.  The more rigorous proofs can be done when you learn calculus.  For now, just need to know that $a^x$ is increasing if $a>1$, and decreasing if $0<a<1$.

Picture of Tina Jin
Re: A Question on a Function
by Tina Jin - Saturday, 1 July 2023, 9:29 PM
 
Thanks! I understand now.