This week, the most important thing that I learned in Math 10 was function notation. I chose this as the most important thing from the relations and functions unit because I think that it can be useful for many expressions that involve functions and the names for each function make it easy to keep track of and differentiate functions, therefore allowing you to solve problems involving multiple functions. Functions are the rule that connects an independent variable to a dependent variable and being able to find the missing input or output is one of the most vital skills to have from this unit because it provides you with more information and you can’t find out anything about the graph if you don’t have the inputs and outputs. It is also important to be able to solve for x or y in relations, but if you know how function notation works, you will be able to solve relations as well as functions, as the name multiplied by the input in a function is equivalent to y. Function notation is an extremely useful tool because having names for the functions allow you to put them in any equation, and I hadn’t previously known how you could involve multiple functions in an equation.

Step 1: The first step to finding a missing input or output using function notation is to identify the parts of the function. The three parts in a function are the name, input, and output. It is essential to know which is which in order to solve for the right variable, being either the independent (x) or dependent (y) variable. In function notation, it is also important to know that the name multiplied by the input is equivalent to the output or y.

Step 2: Replace the input or output variables in the function with the input or output numbers given. This is the step where you need to make sure that you know whether you have been given the input number or the output number so that you put it in the right place in the equation.

Step 3: Solve the equation using the function and the given input or output numbers to find the missing variable.

The example above demonstrates how function notation is used to find an output variable, but function notation can also be used to find an input variable when an output number is given as shown in the example below.

Example:

Function: f(x) = -3x+1

f(x) = 5

Step 1: Because we have been given the output, we need to put it into the equation as the output.

5 = -3x+1

Step 2: Next we solve for x to find the input number by isolating the variable. We need to first subtract -1 from each side of the equation and then divide each side by -3.

5-1 = -3x

4 = -3x

Another way that function notation can be used is when the formula involves more than one function such as in the following example.

Example:

Functions:

h(x) = x +5

j(x) = 2x – 2

Question:

h(2) + j(3)

Step 1: The first step is to put the given input numbers into the function.

h(2) = 2+5

j(3) = 2(3) – 2

Step 2: The next step is to solve each equation.

h(2) = 7

j(3) = 6-2

j(3) = 4

Step 3: The final step is to go back to the original question and combine your answers in the way that it asks. This is an addition question so we would add the two numbers together to get our final answer.

h(2) + j(3) = 7+4

h(2) + j(3) =11