Hi there. Here is a guide on function notation in mathematics. This concept kind of has applications but this concept is a part of the algebra toolbox for math students. Some math images rendered with Quicklatex.com. <center><img src="https://cdn.pixabay.com/photo/2021/11/10/18/44/mathematics-6784603_960_720.jpg" /></center> <center><a href="https://cdn.pixabay.com/photo/2021/11/10/18/44/mathematics-6784603_960_720.jpg">Image Source</a></center> ## Topics --- * Why f(x) Notation Instead of y = * Substituting Number Values For x With Function Notation * Advanced Examples * Adding & Subtracting Functions ## Why f(x) Notation Instead of y = --- Suppose you have two equations that have y = to something. Let's say you have `y = x + 2` and `y = 3x + 10`. If you have to substitute `x = 1` into y, which y equation do you choose? The first one or the second one? This is where function notation and `f(x)` comes in. We can rewrite the above equations as `f(x) = x + 2` and `g(x) = 3x + 10`. Instead of saying substitute `x = 1` into the function `f(x)` we can say obtain the value of `f(1)` (pronounced f of 1). Function notation is a compact and simplified way of substituting values of x in different equations and functions. ## Substituting Number Values For x With Function Notation --- Let's take at some example of function notation with substituting numbers for x. **Example One** Let `f(x) = 5x - 7`, what is the value of `f(10)`? Replace the variable `x` with the number 10. Then apply order of operations to get the answer of 43 `(50 - 7)`. **Example Two** What is the value of g(-2) if `g(x) = x^2 - 7`? <center>https://quicklatex.com/cache3/14/ql_18f41162e16587679e3a9dedad21cf14_l3.png</center> **Example Three - Exponential Function** Evaluate `h(3)` if `h(x)` is ten to the power of x. <center>https://quicklatex.com/cache3/55/ql_3639fa64285ac599cca953ab07c1eb55_l3.png</center> <center><img src="https://cdn.pixabay.com/photo/2021/11/10/18/54/mathematics-6784625_960_720.jpg" /></center> <center><a href="https://cdn.pixabay.com/photo/2021/11/10/18/54/mathematics-6784625_960_720.jpg">Image Source</a></center> ## Advanced Examples --- The idea of function notation is not super complicated but some examples can get a bit technical and algebra intensive. Here are a few tougher examples. **Example One** In `f(x) = 5x + 2`, what is `f(2x)`? At first this looks confusing. What you have to do is replace the input `x` with the new input of `2x`. <center>https://quicklatex.com/cache3/97/ql_fc34cd114fe1a92b67228c9830719497_l3.png</center> **Example Two** In `g(x) = 2x - 1`, what is `g(x + 7)`? Replace `x` with the new input of `x + 7`. Afterwards use algebra techniques to expand and simplify. <center>https://quicklatex.com/cache3/92/ql_c32aad7a186db62e5a4d00b5427ad592_l3.png</center> <center><img src="https://cdn.pixabay.com/photo/2016/11/23/15/51/book-1853677_960_720.jpg" /></center> <center><a href="https://cdn.pixabay.com/photo/2016/11/23/15/51/book-1853677_960_720.jpg">Image Source</a></center> ## Adding & Subtracting Functions --- This concept of adding and subtracting fractions is a natural extension of function notation. I could write another post dedicated to this but I have decided to put some stuff here. You can combine adding & subtracting functions with evaluating them given a value of x. **Example One** If `f(x) = x - 7`, what is the value of `f(1) - f(3)`? The value of `f(1)` is negative 6 and the value of `f(3)` is negative 4. When you compute `f(1) - f(3)` it is `-6 - -4`. The answer here is negative two. <center>https://quicklatex.com/cache3/8b/ql_ef85a35b15ae8b56ab176c3939d6558b_l3.png</center> **Example Two** With `f(x) = 2x + 1` and `g(x) = x - 3`, what is the value of `f(1) + g(3)`? From the function `f(x)` the value of `f(1)` is 3. The value of `g(3)` is 3 minus 3 which is equal to 0. Adding the values of `f(1)` and `g(3)` is 3 plus 0 which gives the answer of 0. <center>https://quicklatex.com/cache3/2b/ql_7f37ea9887d0fd54203f051ce03ff02b_l3.png</center> <center><img src="https://cdn.pixabay.com/photo/2016/03/26/05/14/fractal-1280077_640.jpg" /></center> <center><a href="https://cdn.pixabay.com/photo/2016/03/26/05/14/fractal-1280077_640.jpg">Image Source</a></center> <center>Thank you for reading.</center> Posted using [STEMGeeks](https://stemgeeks.net/@dkmathstats/function-notation-in-math)
| author | dkmathstats |
|---|---|
| permlink | function-notation-in-math |
| category | hive-163521 |
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