# <span style="color:blue"> Functions </span> Functions are one of the crucial ideas in mathematics and computing. --- ## So, what is a function? ### You may have seen these before in a math class. --- # <span style = "color:blue"> Example </span> ## $$ f(x) = x^2 $$ --- # <span style = "color:blue"> Example </span> ## $$g(x) = 3x$$ --- # <span style = "color:blue"> Important Property </span> #### <span style = "color:red"> Evaluate </span> ##### $$g(x) = 3x$$ at $x = 2$. --- $$g(2) = 6$$ --- Explanation: Just replace $x$ with $2$: $g(2) = 3 \cdot 2 = 6$. --- # <span style = "color:blue"> Example </span> ## $$A(t) = 2^t$$ --- # <span style = "color:blue"> OK Go </span> ## If $$A(t) = 2^t, $$ what is $$A(3)?$$ --- # <span style = "color:blue"> OK Go </span> #### If $$A(t) = 2^t, $$ what is $$A(3)?$$ #### <span style = "color:green"> Answer: </span> $$A(3) = 2^3 = 8$$. --- # <span style = "color:blue"> Careful! </span> Not everything you have seen in previous math classes is a function: ## <span style = "color:red"> Not a Function: </span> $$A^2 + B^2 = C^2$$ ### Why not? It isn't clear what to calculate. Do I plug in for $A$, $B$ or $C$? In a function, it should be clear what the input is, and how to use that input to get the output. --- # <span style = "color:magenta"> You Try It! </span> 1. Go back to the asynchronous class folder in Blackboard. 2. Click on the "Examples of Math Class Functions" Checkpoint. 3. Give me at least one example of a function you know from a previous math class (or can adapt from the previous examples) ---