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Introduction to Functions
Introduction to Functions — from OpenStax Precalculus 2e.
Introduction to Functions
Toward the end of the twentieth century, the values of stocks of internet and technology companies rose dramatically. As a result, the Standard and Poor’s stock market average rose as well. The graph above tracks the value of that initial investment of just under $100 over the 40 years. It shows that an investment that was worth less than $500 until about 1995 skyrocketed up to about $1,100 by the beginning of 2000. That five-year period became known as the “dot-com bubble” because so many internet startups were formed. As bubbles tend to do, though, the dot-com bubble eventually burst. Many companies grew too fast and then suddenly went out of business. The result caused the sharp decline represented on the graph beginning at the end of 2000.
Notice, as we consider this example, that there is a definite relationship between the year and stock market average. For any year we choose, we can determine the corresponding value of the stock market average. In this chapter, we will explore these kinds of relationships and their properties.
Tagad tu Neviens kalkulators nenoslīgst šo, bet tā gabali ir komplējami. Izmēģiniet vienu zemāk vai ievadiet paši savu.
Bezmaksas konts pievieno piezīmes par katru nodarbību, ierakstu par to, ko esat pabeidzis, jūsu atrisinātās problēmas vienā vietā, un pasniedzēju, kuru varat jautāt par šo lapu. Pati matemātika ir pieejama ikvienam, kas ir vai nav parakstījies.
Pierakstīties PieteikšanāsŠeit izmantotie simboli
Piesitiet visiem simboliem, kas apzīmē pilnu definīciju, attēlu un ko katrs burts tajā nozīmē.
Jautājumi, ko cilvēki vaicā
What is a function, really?
A rule that assigns exactly one output to each input. The vertical-line test on a graph is the same idea: no input may have two outputs.
Why do we need complex numbers?
Because x² + 1 = 0 has no real solution, and allowing one new number i with i² = −1 makes every polynomial equation solvable. They then turn out to describe rotation, waves and alternating current more naturally than real numbers do.
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Vairāk Precalculus
Complex numbersPolynomial functionsRational functionsSequences and seriesThe binomial theoremConic sectionsVectorsExponential and logarithmic functionsPolynomial division and the remainder theoremParametric equations and polar coordinates