For instance, your graphing calculator will list different functions as y1, y2, etc, so you can tell the equations apart when, say, you're looking at their values in table. In either notation, you do exactly the same thing: you plug −1 in for x, multiply by the 2, and then add in the 3, simplifying to get a final value of +1.īut function notation gives you greater flexibility than using just " y" for every formula.
#Solve for x and y in geometry plus
Now you say " f ( x) = 2 x + 3 find f (−1)" (pronounced as " f-of- x equals 2 x plus three find f-of-negative-one"). You used to say " y = 2 x + 3 solve for y when x = −1". For functions, the two notations mean the exact same thing, but " f ( x)" gives you more flexibility and more information. The same is true of " y" and " f ( x)" (pronounced as "eff-of-eks"). Variables are more flexible, easier to read, and can give you more information. In other words, they switched from boxes to variables because, while the boxes and the letters mean the exact same thing (namely, a slot waiting to be filled with a value), variables are better. Why did your teachers switch from boxes to variables? Well, think about it: How many shapes would you have to use for formulas like the one for the area A of a trapezoid with upper base a, lower base b, and height h? The formula is as follows: Once you got older, your teacher started giving you worksheets containing statements like " x + 2 = 4" and told you to "solve for x". Your teacher gave you worksheets containing statements like " + 2 = 4" and told you to fill in the box. Think back to when you were in elementary school. But function notation also allows you to point out the input variable - being the x inside the parentheticals of f ( x) and g( x).
Instead of naming every function " y", function notation allows for a variety of names, such as f( x) and g( x), much as your calculator names the various formulas you've entered as Y1, Y2, and so forth.
() = įor instance, the formula for the circumference C of a circle, in terms of the value of the circle's radius r, can be written as C = 2π r or, in function notation, it can be written as C( r) = 2π r.
0 kommentar(er)
