# FUNCTION NOTATION AND EVALUATION

## About "Function notation and evaluation"

Function notation and evaluation :

Function notation is the way in which a function can be represented. It is the simple way of giving information about the function without a lengthy written explanation.

## Function notation and evaluation

The most popular and widely used function notation is f(x) which has to be read as "f" of "x".

Important note :

Here "f" and "x" are NOT multiplied.

Always functions are referred to by single letter names, like  f, g, h and so on. Any letter can be used to name a function.

Let us consider the brightness of an electric bulb.

Let "f" stand for the brightness of the bulb and "x" stand for the voltage of electricity given to the bulb.

Here "f" depends on "x".

More clearly, the output of "f" (brightness) is depending on "x" (voltage).

So it will be written as f(x). When we plug some value for "x" (input), accordingly we will get some value for "f" (output).

It has been illustrated in the given figure. Let us look at some more examples.

f(x) = 3x² + 5, g(x) = 3x - 7,  h(x) = ax² + bx + c, s(t) = 1/t

Instead of f(x), sometimes we will be representing a function by "y".

That is,  y  =  f(x)

Then the function f(x)  =  5x + 6 will become y = 5x + 6

Here, the value of "x" is input and the value of "y" is out put.

The equation of a graph is mostly represented as y = f(x) and in the ordered pair (x,y), "x" stands for the value on x- axis and "y" stands for the value on y-axis.

Note :

The notation f : X ----> Y tells us that "f" is the rule which are mapping the elements from the set X to set Y.

The arrow has to be read as " mapped to"

## Applications of function notation

1.Since different functions are represented using different variables like f, g, h, it avoids confusion as to which function is being examined.

2. It allows us to quickly identify the independent variable.

For example, in the function f(x) = ax² + bx + c, the independent variable is "x".

3. It allows to quickly state which element of the function has to be examined.

For example, in the function f(x) = 4x + 5, if the question says "find f(3)", we can understand that we have to find the value of "y" when x = 3

## Evaluating functions - Examples

Example 1 :

Evaluate f(4) where f(x) = 3(2x+1)

Solution :

To evaluate f(4), we have to plug x = 4 in f(x).

Then, we have

f(4)  =  3[2(4) + 1]

f(4)  =  3[8 + 1]

f(4)  =  3 x 9

f(4)  =  27

Example 2 :

Evaluate f(w+2) where f(x) = x² + 3x + 5

Solution :

To evaluate f(w+2), we have to plug x = w in f(x).

Then, we have

f(w+2)  =  (w+2)² + 3(w+2) + 5

f(w+2)  =  w² + 2² + 2w(2) + 3w + 6 + 5

f(w+2)  =  w² + 4 + 4w + 3w + 6 + 5

f(w+2)  =  w² + 7w + 15

Example 3 :

Given f  =  x² - x - 4, if f(k)  =  8, what is the value of "k" ?

Solution :

Set the function rule to 8 and solve for "k".

Then, we have

x² - x - 4  =  8

Subtract 8 on both sides

(x² - x - 4) - 8  =  8 - 8

x² - x - 12  =  0

(x + 3)(x - 4)  =  0

x + 3 =0 ; x - 4 = 0

x  =  -3 ; x  =  4

Hence, the value of can be either 4 or -3.

After having gone through the stuff given above, we hope that the students would have understood "Function notation and evaluation".

Apart from the stuff given above, if you want to know more about "Function notation and evaluation", please click here

Apart from "Function notation and evaluation", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments... WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6