MATH FUNCTIONS GRADE !!

domain

the range on the x-axis

range

the range on the y-axis

when given coordinates, how do you write domain and range.

for example, (3,2),(5,3),(4,9)

you put XE AND YE OUTSIDE BRACKETS-

for ex: XE(3,4,5) YE(2,3,9)

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when writing domain and range, what order do you go by

smallest to greatest

when a number repeats itself what do you do.

For example: (3,9),(3,8),(4,2)

You do not write the number again

For example: XE(3,4) YE(2,8,9)

state domain and range of Y=4

(XER)

(YER| y = 4)

state domain and range of x=2

(XER|x=2)

(YER)

when do you use XE/YE outside brackets vs. (XER)/(YER)

you use XE/YE when given points and you use (XER)/(YER) when given an equation or a graph that doesn’t tell you to state coordinates one by one

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what does that dot mean

function/graph stops at this point and can equal to this point.

what does that open dot mean?

function/graphs stops near this point but can never equal that point.

for example if that dot stops at 3, that means the graph can equal anything leading up to 2.9 but not 3

name parent function:

f(x) = x squared

quadratic function

name parent function:

square root

name parent function:

f(x) = |x|

absolute function

name parent function:

f(x) = 1/x

reciprocal function

name parent function:

f(x)= x

linear function

which functions has asymptotes

recipricol

how do you write domain and range for a recipricol function

state asymtotes for example: (xer| X≠ 1)

(yer| x≠ 1)

how do you determine domain and range of a parabola equation.

you look at “c” value and “a” value

for example if -2(x-4)squared + 5

* (xer)
* (yer| y ≤ 5)

what makes a relation a function

everything in graphing is called a relation, what makes it a function is a set of x and y values, for every x value it has one unique y value.

which graph function cant have zero’s

the reciprocal function cant have zeros in its denominator

which graph fucntion cant have negative numbers

the square root function cant have negative numbers

Function notation:

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if f(x) = 2x-1

figure out: f(3x+5).

What are you substituting?

on the second line, we are substituting whatever is inside the bracket beside “f” which is 3x+ 5 into the expression on the left hand side into “x” on the first equation line.

it becomes: f(3x+5) = 2(3x+5) -1

when substituing for example:

f(2) = 2x-1

what do you have to remember

line up the equal sign!! (remember this in inverse fucntions to when substituting.

look over and do again

Do question c and f (revision)

how do you get rid of a fraction? for example: how would you isolate y

1y/2

you can divide 1/2 to 1y/2 or multiply by 2 to 1y/2

what is the inverse of a function

the reverse of the original functions

what should you remember when balancing equations and isolating for a variable.

you must do the same for both sides to even out the equation. say there is a negative 10 on one side and you want to get rid of it. you have to add 10 to that side and do the same to the other side.

find the inverse of this equation:

f(x) = 2x - 3

first step: change it to y= mx+ b format

y= 2x - 3 --This is the original equation

second step: switch the variable position

x= 2y - 3

third step: solve for y

x+ 3 = 2y

(x+3)/2 = y

this is the inverse equation

find inverse:

2y -10 = 5x

answer is:

2(x-5)/5

compare these two equations:

y = 4x - 3 vs f(x) = 4x - 3

when finding its inverse, why can we say “therefore f-1(x)=…” for the second equation but for the first equation we just keep the final answer in the form of “y=…”

because the second one written in a for sure statement that that equation is a function so our final statement can be written as “therefore f-1(x)=…” when we find the inverse.

what is the transformation graph equation?

f(x) = af(k(x-d))+c

State the transformations

a= vertical compression or stretch

if a is bigger then 1 than it is a vertical stretch

if a is smaller then 1 than it is a vertical compression

k= horizontal compression or stretch

if k is bigger than 1 then it is a horizontal compression by a factor of 1/k

if k is smaller than 1 then it is a horizontal stretch by a factor of 1/k

d= horizontal translation, remember anything inside equation you do opposite. For example: if it d is -3 you move 3 units RIGHT on the new graph

c vertical translation

what is the point of chapter 1.6-1.8

It is to understand how transformations (numbers in an equation in a certain placement) will transform the parent function to a new function on the graph. (like see a new type of graph) everything is connected back to the parent functions.

how to tell difference between a and k value

k value is always beside x IN BRACKETSSSSSS or in the FUNCTION. a is outside the funtion

af(k(x- d)) + c

imagine y= 3 then square root x

imagine y= square root 3x

what is different with the transformations

the first one, it is a vertical stretch by a factor of 3 because the 2 is outside the square root which means function so ti is the “a” value.

the second one, it is a horizontal compression of 1/3 because since the 3 is attached to the x inside the square root it is a horizontal transformation. AND BC IT IS, we have to use the reciprocal of 3 to apply to the new graph which is 1/3

state the transformation of y = 1/2x state the transformation of y =1/(2x)

for the first one, the transformations are: vertical compression of 1/2

and for the second one, the transformations are, horizontal compression by a factor of 1/2

when drawing a reciprical graph, what do you have to remember?

to state the asymptotes

how can you tell reciprocal questions apart from the rest with fractions

if the denominator has an x and there’s no square roots,exponents,absolute then its a reciprocal question

Vertical reflection across what axis?

X axis

Horizontal reflection across what axis?

Y-axis

Draw the graph and state the parent function

State domain and range of SQUARE ROOT