Graphs and Graphing


Graph the curves in Exercises 33–42.
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y = 𝓍√4 ― 𝓍²

24–34. Curve sketching Use the guidelines given in Section 4.4 to make a complete graph of the following functions on their domains or on the given interval. Use a graphing utility to check your work.

{Use of Tech} ƒ(x) = x (x -1)e⁻ˣ

{Use of Tech} A pursuit curve A man stands 1 mi east of a crossroads. At noon, a dog starts walking north from the crossroads at 1 mi/hr (see figure). At the same instant, the man starts walking and at all times walks directly toward the dog at s > 1 mi/hr . The path in the xy-plane followed by the man as he pursues the dog is given by the function y = ƒ(x) = s/2 ((x(ˢ⁺¹)/ˢ) /(s+1) - (x(ˢ⁺¹)/ˢ / s-1)) + s/ s² - 1

Select various values of s > 1 and graph this pursuit curve. Comment on the changes in the curve as s increases. <IMAGE>

{Use of Tech} Elliptic curves The equation y² = x³ - ax + 3, where a is a parameter, defines a well-known family of elliptic curves.

c. By experimentation, determine the approximate value of a (3 < a < 4)at which the graph separates into two curves.

Graphs and Graphing

Graph the curves in Exercises 33–42.

y = 𝓍³ (8―𝓍 )

In Exercises 49–52, graph each function. Then use the function’s first derivative to explain what you see.

y = 𝓍²/³ + (𝓍―1)²/³ 

Sketch the graphs of the rational functions in Exercises 53–60.

y= (x + 1) / (x - 3)

Sketch the graphs of the rational functions in Exercises 53–60.

y = (x² + 1) / x                              

Sketch the graphs of the rational functions in Exercises 53–60.

𝓍⁴ ― 1

y = ------------------

𝓍²