By Maud King Murphy
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Comprises key options, talents to grasp, a short dialogue of the tips of the part, and worked-out examples with tips to uncover the answer.
Additional info for A Beginner's Guide to the Stars
If you need to see the worked solution, look at the solutions section that follows the examples and hints. 15. 1. 4 tan(πx/4 + π/2) one-to-one? 2. 4 tan(πx/4 + π/2) is one-to-one. Graph the function and apply the Horizontal Line Test. Find an interval so that the graph of the function on this interval intersects each horizontal line at most once. 16. 3. Check that the function y = f (x) shown in the graph is one-to-one and sketch the inverse function y = f −1 (x). Remember what one-to-one means.
If any of this material seems unfamiliar to you, spend extra time going over the homework problems. Exponential functions are extremely important and frequently arise in applications of Calculus. Take the time to do enough exercises so that this is familiar to you. Key Concept: Deﬁnition of an exponential function An exponential function is a function of the form f (x) = ax where a is a positive real number called the base of the exponential. Study Figure 3 in this section to see how the shape of the graph of an exponential function changes when different values of a are used.
In particular ln(1/x) is only deﬁned for x > 0. 7 Parametric Curves Key Concepts: • Parametric equations • (x, y) coordinates used to represent position of a particle at time t Skills to Master: • Graph parametric curves by hand and by using a graphing device. • Use parametric curves to answer questions about motion in the plane. 7 show how to describe the location of a particle moving along a path in the plane. In this case, the x and y-coordinates of its location can be thought of as functions of time t.
A Beginner's Guide to the Stars by Maud King Murphy