Logarithmic And Exponential Functions
Gbogbo ọrọ náà
The exponential function \(e^x\) and the natural logarithm \(\ln x\) are a matched pair: each undoes the other. Their graphs are mirror images in the line \(y = x\), and each races towards an asymptote it never touches.
In this lesson you will know and use the properties and graphs of the logarithmic and exponential functions, including \(\ln x\) and \(e^x\), and state the equations of their asymptotes.
Ebumnobi
- Know and use simple properties and graphs of the logarithmic and exponential functions, including ln x and e to the power x, and understand that they are inverses of each other.
- Understand the asymptotic nature of these graphs and state the equations of any asymptotes.
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Akwụkwọ Ọmụmụ
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Nnyocha Ọmụmụ
Ekele diri gi maka imecha ihe karịrị na Logarithmic And Exponential Functions. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.
Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.
Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.
- The function e^x and ln x are: A. equal B. inverses of each other C. both negative D. unrelated Answer: B
- The asymptote of y = e^x is: A. x = 0 B. y = 0 C. y = x D. y = 1 Answer: B
- The asymptote of y = ln x is: A. y = 0 B. x = 0 C. y = x D. x = 1 Answer: B
- ln x is defined only for: A. x < 0 B. x = 0 C. x > 0 D. all x Answer: C
- The value of e^0 is: A. 0 B. 1 C. e D. undefined Answer: B
Rue ajuju ndi a n'ime ngwa ahu
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Akụkụ akwụkwọ
Graphs of Logarithmic Functions
Identify the domain of a logarithmic function.
"Algebra and Trigonometry: Graphs of Logarithmic Functions" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/algebra-and-trigonometry/pages/6-4-graphs-of-logarithmic-functions. Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction
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Meecha Ajụjụ Ule Ọmarịcha
Ị chọrọ ime ajụjụ ule ọmarịcha gbasara Logarithmic And Exponential Functions? Budata ngwa Green Bridge CBT iji nweta ajụjụ ule ọmarịcha na nyocha zuru ezu gbasara isiokwu a.
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