1.1: Introduction to Functions and Equations

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Difference Between an Equation and a Function

By Intermediate Algebra Students Andrew Medina and Nelly Kihiu

The difference between an equation and function would be that an equation shows “the equality between two expressions”, as indicated by the article “Difference between Equations and Functions” at www.differencebetween.info, and is good for when we must solve a variable when the problem contains another constant or static variable. Functions differ from equations because they show the relationships between inputs and outputs, where one input for the variable, which can change (being the independent variable “x”), will produce a unique output of a dependent variable “y”. So, functions show the mathematical relationships between inputs and outputs.

For example, these variables could be the human population number pertaining to a certain year. The data sets that hold these numbers could be modeled through quadratic regression that fits the curve of data points and would help us predict the population amount at a future year, where the year is the input variable that outputs the population number. A real-world example of this would be the Nihonmachi Fence at Chiyo’s Garden in Seattle that portrays the “growth, decline, and rebirth” of the Seattle’s Japanese American community. In the picture below, the height of the slats refer to the population of the community at a specific year, which depicts a curve of a function with the year being the input and the population being the output. It begins with the year the first steam ship brought over Japanese immigrants in 1896 as indicated by Wing Luke Museum’s website . The artist would have taken the years and the associated population values and through modeling the data the artist would be able to visualize its mathematical representation and turn it into this public and cultural work of art.

References:

Factoring in Algebra. (n.d.). Retrieved April 17, 2022, from https://www.mathsisfun.com/algebra/factoring.html?msclkid=e2d532edbedc11ec91cf522476311c99 Links to an external site.

Flynn, A. (2018, December 16). How do you use factoring in real life situations? Greedhead.net. Retrieved April 17, 2022, from https://greedhead.net/how-do-you-use-factoring-in-real-life-situations/#How_do_you_use_factoring_in_real_life_situations

Difference between Equations and Functions. Retrieved April 18, 2022 from
http://www.differencebetween.info/difference-between-equations-and-functions

Challenge 6: Is there any Real World reason to factor a quadratic? YouTube Video by MathMachines.
https://www.youtube.com/watch?v=_Tf9FeqUVfM&ab_channel=MathMachines

Wing Luke Museum of the Asian Pacific American Experience. Chiyo’s Garden- Nihonmachi Fence.
http://www.wingluke.org/single-exhibit/?mep_event=759Links to an external site.

Photo of Nihonmachi Fence taken by Alan Alabastro. https://www.alabastrophoto.com/index
Photo source: https://southseattleemerald.com/nihonmachi-fence-2_photo-by-alan-alabastro.

David Arnold. 2.2: Zeros of Polynomials, LibreTexts (2021, February 15). College of the Redwoods.
https://math.libretexts.org/@go/page/58416.