Identify the function rule
Write the input as (x)
Replace (x) with the given value
Simplify using order of operations
Evaluate the output
Write the result as (f(x))
For domain, find allowed input values
For range, find all possible output values
To add functions, compute ((f+g)(x)=f(x)+g(x))
To subtract functions, compute ((f-g)(x)=f(x)-g(x))
To multiply functions, compute ((fg)(x)=f(x)g(x))
To divide functions, compute ((f/g)(x)=frac{f(x)}{g(x)}), with (g(x)neq 0)
To compose functions, compute ((fcirc g)(x)=f(g(x)))
To find the inverse, swap (x) and (y) and solve for (y)
To graph a function, plot input-output pairs
To solve (f(x)=0), find the x-values where the output is zero
To compare functions, check values, graphs, or growth rates
To transform functions, shift, reflect, stretch, or compress the graph