1. Take the function f(X) = (X-1)/X
a. What does this function equal when X = 0, X = 1, and X =2 ?
b. How about when X =100, X = 1000, and X = 10,000?
c. Describe in words what a graph of this function would look like.
d. What would you say the limit of this function is as X approaches infinity? You can use logic or induction rather than a mathematical proof to answer this question. Just explain your logic.
2. Which of the following functions are continuous? Explain your answer for each part.
a. f(X) = 100
b. f(X) = 1 if X >0
f(X) = 0 if X=0 or X<0
c. f(X) = 2X
d. f(X) = 2x if X>0
f(X) = 0 if X=0
f(X) = 2x if X<0
e. f(X) = 5X2 - 3
4. Write an equation for the line that passes through the point (5,4) and has a slope of 2.
5. Which of the following functions are linear? Explain your reasoning.
a. f(X) = 5X + 100000
b. f(X) = 2X2 - 200
c. f(X) = 5
d. f(X) = -551 + 10000X
e. f(X) = X3 - X2
Fifteen problems involving Graphs, Limits, Continuity, Equation of Line from Two Points, Equation of Line from Slope and a Point and Linearity are solved. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.