Function Notation Formula: ƒ(x)
Any function notation formula or equation begins with the symbol ƒ(x). Function notation finds the value of y for a given operation on x.
In algebraic functions, the value of ƒ(x) = y. As an example, the function ƒ(x) = 2x + 5 is the same as the equation y = 2x + 5.
Function Notation Quiz
Instructions: Try the quiz below on using function notation. You may also want to view the examples in the second part of the page.
| [WpProQuiz 17] |
Function Notation Equation – Input and Output
Let’s look at our function again: ƒ(x) = 2x + 5
The value of x that we put into the function notation equation is called the input. The value of ƒ(x) = y is called the output. Input and output values can be positive or negative.
How to Solve Using Function Notation Formula
Example 1:
Place 1 in the function for the input value of x to solve the function ƒ(1):
ƒ(x) = 2x + 5
ƒ(x) = (2 × 1) + 5 = 2 + 5 = 7
So, in the above function notation and resulting equation, when x = 1, the output is 7.
Example 2:
When the input is x = 2, the output is 9:
ƒ(x) = 2x + 5
ƒ(x) = (2 × 2) + 5 = 4 + 5 = 9
So, using function notation, we get the equation from the input and then find the output.
Evaluating the Function
Working out the function notation formula from the inputs to find the outputs is called evaluating the function.
You might see the instructions: “Evaluate the Function” on your exam.
Inverse Functions
Sometimes we have the output and we want to work backwards to discover what the input was.
When we have to work backwards to find the input, we use what is called an inverse function.
Function Notation – Domain and Range
The set of all possible input values for any function notation formula is called the domain. The set of all possible output values for a function is called the range.
Sometimes the domain and range will be specified in the narrative details of the problem. For other exam questions, input and output values may be provided in a chart or table
Function Notation Formula – Advanced Problems
Sometimes you will have to solve one function and use the output from the first function as the input in the second function.
An example of an advanced function notation formula problem is as follows:
For the two functions f1(x) and f2(x), f1(x) = x + 5 and f2(x) = x2.
Step 1:
What is the value of f2(f1(2))?
To solve the problem, our first step is to find the output from the first function for the given input:
Our first function is (f1(2)), so the input for the first function is 2.
f1(x) = x + 5 = 2 + 5 = 7
Step 2:
The second step is to use the output from the first function as the input in the second function
f2(x) = x2 = 72 = 49
So, f2(f1(2)) = 49
Polynomial Functions
Polynomial functions are functions that can be written with coefficients, variables, and exponents. An example of a polynomial function is: f(x) = x2 + 3x + 7
You solve a polynomial function in the same way as any other function.
Solving Polynomial Functions
So, for example, consider the following question:
What is the value of f(x) = x2 + 3x + 7 when x = 3?
Substitute the value of 3 for x to solve the problem.
f(x) = x2 + 3x + 7
f(3) = 32 + (3 × 3) + 7
f(3) = 9 + 9 + 7
f(3) = 25
Trigonometric Functions
Sine, Cosine, and Tangent are the functions used in trigonometry.
If your entrance exam covers advanced math, you should look at our practice problems on trigonometry.
