By David Lippman, Melonie Rasmussen
Precalculus: An research of services is a unfastened, open textbook protecting a two-quarter pre-calculus series together with trigonometry. the 1st part of the booklet is an research of capabilities, exploring the graphical habit of, interpretation of, and suggestions to difficulties regarding linear, polynomial, rational, exponential, and logarithmic services. An emphasis is put on modeling and interpretation, in addition to the $64000 features wanted in calculus. the second one section of the e-book introduces trigonometry. Trig is brought via an built-in circle/triangle process. Identities are brought within the first bankruptcy, and revisited all through. Likewise, fixing is brought within the moment bankruptcy and revisted extra greatly within the 3rd bankruptcy. As with the 1st a part of the publication, an emphasis is put on motivating the techniques and on modeling and interpretation.
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Extra resources for Precalculus: An Investigation of Functions
A point where a function changes from concave up to concave down or vice versa is called an inflection point. Example 10 An object is thrown from the top of a building. The object’s height in feet above ground after t seconds is given by the function h(t ) 144 16t 2 for 0 t 3 . Describe the concavity of the graph. Sketching a graph of the function, we can see that the function is decreasing. We can calculate some rates of change to explore the behavior t h(t) 0 144 1 128 2 80 3 0 Rate of Change -16 -48 -80 Notice that the rates of change are becoming more negative, so the rates of change are decreasing.
3 Rates of Change and Behavior of Graphs 37 F (6) F (2) = 62 2 2 2 2 6 2 62 2 2 36 4 4 16 36 4 1 Newtons per centimeter 9 Simplifying Combining the numerator terms Simplifying further This tells us the magnetic force decreases, on average, by 1/9 Newtons per centimeter. Equivalently, it tells us the magnetic force decreases, on average by 1 Newton for each 9 centimeters the distance increases. Example 6 Find the average rate of change of g (t ) t 2 3t 1 on the interval [0, a] .
The inside function in the composition is s(3). Since the input to the s function is time, the 3 is representing 3 minutes, and s(3) is the number of sit-ups that can be done in 3 minutes. Taking this output and using it as the input to the c(s) function will gives us the calories that can be burned by the number of sit-ups that can be done in 3 minutes. Note that it is not important that the same variable be used for the output of the inside function and the input to the outside function. However, it is essential that the units on the output of the inside function match the units on the input to the outside function, if the units are specified.