Abaddon angel of destruction wrote:
k now i’m stuck on a review problem that i forgot how to do: y=2/x/
^those thingies are supposed to be absolute value, and its x intercept
X intercept of y=2|x|? Just do the math like any equation, y=0
so 0=2|x|
In this case you don’t have to worry about the absolute value sign for now, but later on you’ll have things like y=2|x-6|-2. You’ll just have to know how the graph changes with the 2, -6, and -2 added in from the normal y=|x|, but that’s later on.
so the x intercept is zero too? wait i’m lost can you explain in a simpler form?
You just treat the graph as y=2x. In this case it changes how the graph shapes but doesn’t change the intercept. So yes it’s zero.
Abaddon angel of destruction wrote:
k now i’m stuck on a review problem that i forgot how to do: y=2/x/
^those thingies are supposed to be absolute value, and its x intercept
X intercept of y=2|x|? Just do the math like any equation, y=0
so 0=2|x|
In this case you don’t have to worry about the absolute value sign for now, but later on you’ll have things like y=2|x-6|-2. You’ll just have to know how the graph changes with the 2, -6, and -2 added in from the normal y=|x|, but that’s later on.
so the x intercept is zero too? wait i’m lost can you explain in a simpler form?
You just treat the graph as y=2x. In this case it changes how the graph shapes but doesn’t change the intercept. So yes it’s zero.
(0,0)? andfor 24, y=/x-3/
y=3 y=-3
x=-3 x=3?
__________________
“You’ll never know how strong you really are until being strong is the only choice you have left”
I do not know if it has already been mentioned but will give you some tips....
(sorry english is not my main language so I apologize about the grammar flaws)
I do not know if you already know them but it does not damage if I mention them again.
First case
y=|x plus b|
b= any positive number
I.E
1,2,4,5,etc to infinite
y=|x plus b|< — — -When you have this case
b Indicates the point of the interception in the horizontal line and the interception point is always going to be in the neg. side (the left one before 0)
with the value of b.
Example if it is
y=|x plus 1|
The point is going to be in -1
y=|x plus 2|
The point is going to be in -2
y=|x plus 3|
The point is going to be in -3
etc...
the angle inclination of the “V” is the same always
For example in the case
y=|x plus 1|
You are going to start your graphic at (-1,0) [using the formula (x,y)
Where x is the horizontal line and y the vertical line
When X is -1 Y is 0
When X increases or loses one Unite Y is going to grow one unite
So
When X is -2 or 0 .... Y is going to be 1
In this case Y is always going to grow positive, never negative.
The same will happen but in a proportional way with any number like 2 3 etc.
Other example
y=|x plus 2|
The point is going to be found in (-2,0) [again same (x,y)]
WHen x is -2 y is 0
When x is -4 or 0 Y is going to be 2
The y is going to grow 2 by 2, if it were =|x 3| it would grow 3 by 3.
Second Case
y=|x-b|
Same rules as the first cae but now your point is always going to be in the positive side.
Example:
y=|x-2|
The point is going to be found in (2,0) [again same (x,y)]
WHen x is 2 y is 0
When x is 4 or 0 Y is going to be 2
The y is going to grow 2 by 2, if it were =|x-3| it would grow 3 by 3.
Third Case
y=|x*b| or y=b*|x|
^In this case always the origin point or inter point is going to be in (0,0)
b= again is any number in this case it can be any real number
Do not forget the “V” starts always in (0,0)
And one more time the value of y is going to depend in the X
For example
y=|x*1| or y=1*|x|
When X is 0 y is going to be 0
If X is 1 or -1 Y is going to be 1
If X is 2 or -2 Y is going to be 2
and the same way with any other number.
Other example
y=|x*2| or y=2*|x|
When X is 0 y is going to be 0
If X is 1 or -1 Y is going to be 2
If X is 2 or -2 Y is going to be 4
Y is going to be two times X
In this case you will notice that when you use greater numbers the lines inclination is going to tend to be more vertical.
If you use a value like one the inclination angle is going to be visible, but if the value is 1000 or more till the infinite
You will see that the lines are almost vertical.
Fourth Case
y=|x/b|
In this case as in the multiplication case the origin is going to be in (0,0)
And Y is going to be equal to the value of x divided by “b”
Example
y=|x/1|
If the X is 1 or -1 Y is going to be 1
If X is 2 or -2 Y is going to be 2
If X is 3 or -3 Y is going to be 3
etc.
Other Example
y=|x/2|
if X is 1 then Y 1/2 = 0.5
if X is 2 then Y is 2/2= 1
if X is 3 then Y is 3/2 = 1.5
etc.
In this case when you use bigger numbers the lines inclinatio are goint to tend to be more horizontal (opposite multiplication)
Fifth Case
y= |root of b|
Any positive number well...
This one is easy
Y is always going to be = root of b
And X is any point from -infinit to infinit
As result you have always an horizontal line where Y is equal always to root of b
Sixth Case
y= |b^c|
b= any positive number
c= any positive number
X is also any point from -inf to inf
While Y is always going to be equal to b^c
Seventh Case
y= |root of x|
Any positive number well...
This one is easy
Y is always going to be = √x
And X is any point from (0, inf)
Example Y=root of 4 Y = 2
As result you have a root graphic
8 case
y= |x^2|
The origin is always (0,0)
And you have a parabola
9 case
y= |1/x|
Well I do not think you will need this case but you have an amazing graphic with this one.
Also I do not think you need the log case or the y=(√x/x b) case or similar stuff :P
Well forgive me if I am saying something stupid or that does not have to do with your doubts.. it is late and my brain is not working properly and needs to sleep. I am not even sure what you want exactly, but if the tips help you I will be happy anything else you can ask me and I will see how can I help.
If something is wrong or everything is totally wrong tell me and I will fix it.
See ya and Good luck!
If the info helps you it would be nice if you can give me a good rep vote :P na do not belive me it is just a joke I do not want anything but a good rep point would be nice.
Abaddon angel of destruction wrote:
for the following functions tell whether the graph opens up or down, find the vertex, and tind the axis of symmetry:
y=-3x2 1
Didn’t I go over this with ya? xD
The axis of symmetry is what X equals at the vertex. I.E. if the vertex is (1,5) the axis of symmetry is x=1
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