You will create a piecewise function of two individual functions (pieces), one piece defined for x <  2 and the other piece defined for x ≥ 2. using the first letter of your first name, create a function of the type for that letter (listed below) for the region x <  2. using the first letter of your last name, create a function of the type for that letter (listed below) x ≥ 2. these two pieces then make up the piecewise function you will use for your main discussion post.
abc:   polynomial of degree greater than 2
def:   rational function
ghi:  algebraic function with a root
jkl:  exponential function, but not “the” exponential function of base e
mno:  exponential function, base e
pqr: logarithmic function, but not the natural log
stu: natural log function
vwx:  trigonometric function
yz:   inverse trigonometric function
use the free graphing utility at desmos to create a graph of your piecewise function and include this graph in your main post. the syntax for entering a piecewise function at desmos is y = {condition 1: rule 1, condition 2: rule 2). an example of this is y = { x <  0:  sin(2x), x >  = 0:  2x + 1/3 }.
desmos site, graph sample.
think of this as a math report. you will define your piecewise function, include a graph of it, state the domain and range, evaluate the limit as x approaches 2, and evaluate the limit as x approaches infinity. your write-up should include proper mathematical notation and justification for all work and answers, both mathematical and verbal.
to get an image of your graph at the desmos site, you must first save it as an image file to your own computer. you can then include the image in your post. note the drop down menu and the image feature available at desmos.