By David Lippman, Melonie Rasmussen

Precalculus: An research of capabilities is a unfastened, open textbook masking a two-quarter pre-calculus series together with trigonometry. the 1st section of the ebook is an research of capabilities, exploring the graphical habit of, interpretation of, and strategies to difficulties concerning linear, polynomial, rational, exponential, and logarithmic features. An emphasis is put on modeling and interpretation, in addition to the $64000 features wanted in calculus. the second one component to the publication introduces trigonometry. Trig is brought via an built-in circle/triangle procedure. Identities are brought within the first bankruptcy, and revisited all through. Likewise, fixing is brought within the moment bankruptcy and revisted extra commonly within the 3rd bankruptcy. As with the 1st a part of the publication, an emphasis is put on motivating the recommendations and on modeling and interpretation.

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**Extra info for Precalculus: An Investigation of Functions **

**Sample text**

35. 36. Use a graph to estimate the local extrema and inflection points of each function, and to estimate the intervals on which the function is increasing, decreasing, concave up, and concave down. 37. f ( x) x 4 4 x 3 5 38. h( x) x 5 5 x 4 10 x 3 10 x 2 1 39. g (t ) t t 3 41. m( x) x 4 2 x 3 12 x 2 10 x 4 40. k (t ) 3t 2 / 3 t 42. 4 Composition of Functions Suppose we wanted to calculate how much it costs to heat a house on a particular day of the year. The cost to heat a house will depend on the average daily temperature, and the average daily temperature depends on the particular day of the year.

Example 6 Given f (t ) t 2 t , evaluate f (3) and f (2) f (3) 3 2 3 f (2) (2) 2 (2) We could simplify the results above if we wanted to f (3) 32 3 9 3 6 f (2) (2)2 (2) 4 2 6 We are not limited, however, to putting a numerical value as the input to the function. We can put anything into the function: a value, a different variable, or even an entire equation, provided we put the input expression everywhere we see the input variable. Example 7 Using the function from the previous example, evaluate f(a) This means that the input value for t is some unknown quantity a.

We could make an educated guess at a maximum reasonable value, or look up that the maximum circumference measured is 163 feet1. With this information we would say a reasonable domain is 0 c 163 feet. Similarly for the range, it doesn’t make sense to have negative heights, and the maximum height of a tree could be looked up to be 379 feet, so a reasonable range is 0 h 379 feet. Example 2 When sending a letter through the United States Postal Service, the price depends upon the weight of the letter2, as shown in the table below.

### Precalculus: An Investigation of Functions by David Lippman, Melonie Rasmussen

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