Group C

How to Sketch the Graph of an Equation  Graph of Equation: The set of all solution points of an equation 1. Rewrite the equation so that one of the variables is isolated on one side 2. Make a table of several solution points 3. Plot these points in the Cartesian plane 4. Connect the points with a smooth curve

Example 1 x y=x First, make a table of values by choosing values of x and calculating the values of y Now plot the corresponding points

Using a Graphing Utility 1. Rewrite the equation so y is isolated 2. Enter the equation into the utility 3. Determine a viewing window that shows all important features of the graph 4. Graph equation

Example 2: Sketching a Circle Using a Graphing Utility  The graph of x 2 + y 2 = 9 is a circle whose center is at the origin and radius is 3. To graph the equation, solve for y.  x 2 + y 2 = 9  y 2 = 9 - x 2  y = √9 - x 2  The graph of y = √9 - x 2 is the top half  The graph of y = -√9 - x 2 is the bottom half

x 2 + y 2 = 9 Enter both equations into the calculator and generate the graph. If you use the standard viewing window the graph may not appear to be a circle, by changing the viewing window to a square setting you can overcome this.

Example 3: Real life  A runner runs a constant rate of 4.9 mph. (Distance = Rate x Time)  d = 4.9t a) Determine how far a runner can run in 3.1 hours b) How long will it take to run a 26.2 mile marathon?

Example 3: Real life a) Substitute 3.1 hours for t d = 4.9(3.1) d = 15.2 miles In 3.1 hours the runner could run 15.2 miles b) d = Rt d/R = t 26.2m / 4.9mph = t t = 5.3 hours  It would take about 5.3 hours to run a 26.2 mile marathon