In this episode of Engineer In Training Exam TV, Justin walks you through a Fundamentals of Engineering Exam Review of Functions.

The goal is to reinforce both your understanding of functions as well as function notation, two topics commonly encountered on the Engineer In Training Exam.

He will first start with defining a function and function notation, then discuss how to evaluate a function, discuss domain and range, and wrap it up with a discussion on function composition.

This Fundamentals of Engineering Exam Review of Functions is part of the global subject Mathematics.

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Hey what’s gong on everyone, it’s Justin Dickmeyer from EngineerInTrainingExam.com.

In today’s quick tutorial we are going to present a Fundamentals of Engineering Exam Review of Functions.

We’ll start off by defining a function and function notation, discuss how to evaluate a function, define domain and range and then finish off with function composition.

So let’s start off our Fundamentals of Engineering Exam Review of Functions by defining exactly what a Function is.

An equation will be a function if for any X

in the domain of that equation the

equation will yield exactly one value of

y so the definition criteria for an

equation to be a function is for all X

in that domain there’s only one value of

y so if we can satisfy this with an

equation then that equation is a

function so let’s let’s illustrate that

look at y is equal to x squared plus 1

so is this a function quickly I would

say yes this is a function because given

any X there is only one way to square it

and then add one to the result so no

matter what value of x we plug in here

there’s only going to be one value of y

one value of Y satisfies our criteria so

this is a function let’s look at Y

squared is equal to X plus 1 for the

second equation the only difference is

that we move the exponent off the X and

onto the Y this small change is all that

is required in this case to change the

equation from a function to something

that isn’t a function we can see that

this isn’t a function fairly simply by

plugging in any X let’s just plug in 3

and solve for so Y squared is equal to 3

plus 1 which is equal to 4 let’s solve

for y and we see that it’s going to be

plus or minus 2 that’s two values of Y

it does not satisfy our definition

criteria for function so this is not

this equation is not a function so let’s

talk function notation

function notation is nothing more than

an elaborate way of writing y so from so

let’s look at the equation y is equal to

2x squared minus 5x plus 3 so if we want

to write this equation using function

notation we can substitute the Y as f of

X we can substitute it as G sub X we can

substitute as H of X etc we just plug in

what’s on the right side and that’s

function notation so recall that this is

not some letter say f multiplied by X

it’s just like I said an elaborate way

of writing y using function notation

allows us to represent the value of the

function at a given X within a domain in

a clean and compact way so how do you

evaluate a function let’s take that same

function f of X is equal to 2x squared

minus 5x plus 3 and so what to evaluate

this wherever we see an X on this left

side we plug in whatever X we decide to

plug into the function on the left side

so let’s take f of negative 3 and just

plug it in on the right side it’s that

simple

and then use a math we’ll just go ahead

and quickly solve that just trust me

that it equals 36 so let’s talk about

domain and range this is one of the more

important concepts of a function the

domain of a function is the set of all

values of x all values that can be

plugged into a function and have the

function exist and have a real number

for a value so the domain we need to

avoid anything of division by zero we

need to avoid square roots of negative

numbers logarithms of 0 etc or anything

that makes a function non existent the

range of a function is simply the set of

all possible values that a function can

so let’s quickly find the domain of a

function let’s say we have f of X is

equal to X minus 4 divided by x squared

minus 2x minus 15 so in this case we

want to avoid division by 0 so let’s

isolate x squared minus 2x minus 15 and

since we don’t want it to be a division

by 0 we have to determine what values of

x will make that equal to 0 so let’s set

this function equal to 0 factor it X

minus 5x plus 3 and we can solve that

and see that X is equal to negative 3

and X is equal to 5 so the domain for

this function the domain will be all

values of X except X equal negative 3

and X equal 5

so let’s talk about function composition

let’s say we have two functions f of X

and we have G sub X the function

composition of f of X and G sub X can be

written as f G sub X which is equal to F

with G sub X plugged into that function

so in other words compositions are

evaluated by plugging in the sex second

function which in this case is G sub X

into the first function which is f of X

so let’s look at an example here let’s

take that same composition of F G sub X

and let’s use the equation so let’s say

we have f of X is equal to 3x squared

minus X plus 10 and let’s say we have G

sub X is equal to 1 minus 20 X so all we

need to do is plug G sub X into f of X

so this will equal 3 120 x squared minus

120 X plus 10 so we can solve that out

just trust me that it’s going to come

out to 12,000 12,000 pourtant

interchanging the order will usually

result in a different answer and we can

illustrate that by using the same

functions here let’s use f of X is equal

to 3x squared minus X plus 10 let’s use

G sub X the same one as 1 minus 20x this

time let’s plug f of X and the G sub X

and see what we get

that will come out to be G sub 3 x

squared minus X plus 10 which is equal

to 1 minus 23 x squared minus X plus 10

which is equal to minus 60 x squared

plus 20x minus 199 so to compare that to

the previous example we see that by

interchanging the same functions that

we’ve got two different answers so

that’s all I got for you guys today I

hope you guys enjoyed that quick review

I know it was a fundamental and that you

probably right up on this stuff but I

just wanted to touch briefly on it so

check out my website at engineering

training exam com for more resources and

leadership I look forward to meeting

guys and getting getting to know you and

help you on your journey as you take on

and prepare for the engineering training

exam

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