What is equation notation
In general, a function is represented using the letter 'f'. Also, other lower case letters such as 'g' or 'h' are also used to represent the function. This equation tells us that y is dependent on x, because y is the square of x. In technical terms, y is a function of x , and this is specified using function notation formula as follows:. Let's look into some examples to understand the application of the function notation formula.
Example 2: A cone has a variable height h and a variable base radius r , but the sum of h and r is fixed. Express the mass m of cone as a function of its height h. Let the fixed sum of h and r be k. Function Notation Formula Being a critical part of mathematics, functions and function notation formula exists at the center of mathematical analysis studies. What is Function Notation Formula? Let's take an example to understand the function notation formula.
Break down tough concepts through simple visuals. After all, there's no rule saying that y can't be the independent variable. The function name is what comes before the parentheses, so the function name here is g. In the second part of the question, they're asking me for the argument.
But in the second part, they've plugged a particular value in for t. So, in the second part, the argument is the number —1. You evaluate " f x " in exactly the same way that you've always evaluated " y ". Namely, you take the number they give you for the input variable, you plug it in for the variable, and you simplify to get the answer. For instance:. To keep things straight in my head and clear in my working , I've put parentheses around every instance of the argument 2 in the formula for f.
Now I can simplify:. To evaluate, I do what I've always done. I'll plug the given value —3 in for the specified variable x in the given formula:. Once again, I've used parentheses to clearly designate the value being input into the formula. In this case, the parentheses are helping me keep track of the "minus" signs. If you experience difficulties when working with negatives , try using parentheses as I did above.
Doing so helps keep track of things like whether or not the exponent is on the "minus" sign. And it's just generally a good habit to develop. An important type of function is called a " piecewise " function, so called because, well, it's in pieces. For instance, the following is a piecewise function:. Which half of the function you use depends on what the value of x is. Let's examine this:. This function comes in pieces; hence, the name "piecewise" function.
When I evaluate it at various x -values, I have to be careful to plug the argument into the correct piece of the function. Since this is less than 1 , then this argument goes into the first piece of the function. To refresh, the function is this:.
Then I'll be plugging the —1 into the rule 2 x 2 — 1 :. Next, they want me to find the value of f 3. Since 3 is greater than 1 , then I'll need to plug into the second piece of the function, so:.
This is the only x -value that's a little tricky. Which half do I use? Looking carefully at the rules for the functions, I can see that the first piece is the rule for x -values that are strictly less than 1 ; the rule does not apply when x equals 1. On the other hand, the second piece applies when x is greater than or equal to 1. You can use the Mathway widget below to practice evaluating functions at a given numerical value. Try the entered exercise, or type in your own exercise. Then click the button and select "Evaluate" to compare your answer to Mathway's.
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