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    Graphs, Limits, Continuity, Equation of Line from Two Points

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    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

    3. Suppose a line passes through the points (4, 2) and (0,0). Write an equation for this line, and identify the slope and intercept of this line.

    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

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    Solution Summary

    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.