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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.

Zvino iwe Hapana calculator inogadzirisa iyi imwe, asi mapepa ayo anogona kuongororwa. Tsananguro:

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Mubhadharo wakasununguka unowedzera mazita ezvidzidzo, zvinyorwa zvezvidzidzo zvawakati wazvigadzirira, zvidzidzo zvawave uchizvigadzirisa, uye mudzidzisi waungabvunza nezvechidzidzo ichi. Maths inowanikwa kune vese, vasiri vadzidzi kana vadzidzi. Kuwana mazita ezvidzidzo zvinodiwa kunogona kuitwa pawebsite ye Maths.

Kutanga Kupinda

Mazita anoshandiswa pano

Tinya chero chiratidzo kuti uone chirevo chakazara, vhidhiyo, uye kuti chii chinoreva chero chiratidzo.

Mabvunzo vanhu vanobvunza

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.

Zvimwe zvenyaya iyi zvakashandurwa kubva OpenStax Precalculus 2e (CC BY-NC-SA 4.0). Condensed uye re-akaratidza pano; zvikanganiso ndedu. Nekuti chigadzirwa ichi chine mvumo yekushandiswa pasina kutengeswa, ichi chidzidzo chine mukana wekuwana mari, hachina kutengesa, uye chinopihwa pasi pechibvumirano ichi.

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