Function Notation
| Site: | Gladwin |
| Course: | Michigan Algebra I Sept. 2012 |
| Book: | Function Notation |
| Printed by: | Guest user |
| Date: | Saturday, November 23, 2024, 5:21 AM |
Description
Function Notation
Evaluating Functions
Recall from the linear unit that f(x) and y can be used interchangeably and that function notation is a shortened method of writing a function. Functions are represented using parentheses such as f(x). This notation indicates "f" is a function of, or depends on, the variable x. A quadratic equation might be y = x2 + 2x - 4, while the equivalent function would be f( x) = x2 + 2x - 4. Both the equation and the function create the same table and graph. However, function notation states the input and the output at the same time, something the equation cannot do.
The expression f(x) means "plug a value for x into the formula f "; the expression does not mean multiply f and x . In function notation, the x in f(x) is called the argument of the function, or just the argument. When given f(2), it means to replace any x in the function with 2 and then find the function's value.
Example 1
Given f(x) = x2 + 2x - 1, find f(2).
Step 1. Eliminate the input value "x" and replace it with parentheses.
f() = ()2 + 2() - 1
Step 2. Place the input value of 2 inside the parentheses.
f(2) = (2)2 + 2(2) - 1
Step 3. Simplify the right side of the equation.
f(2)= 4 + 4 - 1
f( 2)= 7
Example 2
Given f(x) = x2 + 2x - 1, find f(-3).
Step 1. Eliminate the input value "x" and replace it with parentheses.
f() = ()2 + 2() - 1
Step 2. Place the input value of -3 inside the parentheses.
f(-3) = (-3)2 + 2(-3) - 1
Step 3. Simplify the right side of the equation.
Evaluating Symbolically
Functions can also be evaluated for inputs that are variables or expressions.
Example 1 Given f(x) = 3x2 + 2x, find f(h).
Step 1. Eliminate the input value "x" and replace it with parentheses.
f() = 3()2 + 2()
Step 2. Place the input value of h inside the parentheses.
f(h) = 3(h)2 + 2(h)
Step 3. Simplify the right side of the equation.
Example 2
Given f(x) = 3x2 + 2, find f(2x).
Step 1. Eliminate the input value "x" and replace it with parentheses.
f() = 3()2 + 2
Step 2. Place the input value of 2x inside the parentheses.
f(2x) = 3(2x)2 + 2
Step 3. Simplify the right side of the equation.
f(2x) = 3(4x2)+ 2
f(2x) = 12x2+ 2
Practice
Answer Key
Sources
Embracing Mathematics, Assessment & Technology in High Schools; A Michigan Mathematics & Science Partnership Grant Project
Kuta Software, www.kutasoftware.com/free.html (accessed 07/19/2010).
Stapel, Elizabeth. "Function Notation: Introduction/Evaluation." http://www.purplemath.com/modules/fcnnot.htm (accessed 7/15/2010).