# MATH260 W3 Lab Worksheet

Math 260 - Week 3 Lab

In calculus, much effort is devoted to determining the behavior of the graph of a function over an interval on the Cartesian Plane.

Finding x & y intercepts, asymptotes, intervals of increasing or decreasing, local maximum and local minimum points, concavity/curvature can all be done using Algebra and Calculus.

Using Algebra: · The x and y-intercepts can be found by letting y = 0 then x = 0 respectively.

· Finding the zeros of the denominator of a function gives vertical asymptotes.

Using Calculus: · The limit of the function as x infinity will give horizontal asymptotes.

· The zeros of the first derivative helps to find critical numbers in order to determine

intervals of increasing or decreasing and to find the max and min of a function.

· The zeros of the second derivative helps to find inflection numbers in order to

determine Intervals of upward or downward concavity.

**Graphing with Calculus**

1.) The graph of is above. If you did not have this graph to look at but

wanted to sketch it, name at least three points on the graph and at least two other features of

the graph that would be valuable to know in order to sketch an accurate graph.

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