SOLUTION: Can you pls help me 3.)y=x^2-4x •Graph this original function in its entire domain but coloring green that portion of the graph over the limited domain x>=2, •Find its

Algebra ->  Inverses -> SOLUTION: Can you pls help me 3.)y=x^2-4x •Graph this original function in its entire domain but coloring green that portion of the graph over the limited domain x>=2, •Find its       Log On


   

Question 211263This question is from textbook COLLEGE ALGEBRA
: Can you pls help me
3.)y=x^2-4x
•Graph this original function in its entire domain but coloring green that portion of the graph over the limited domain x>=2,

•Find its inverse over x>=-4,
•On another set of coordinate axes, graph this inverse. Color it blue. On this same set of coordinate axis, graph the original f(x) on the limited domainx>= 2, y>=-4 & color it green.
•Draw the line y = x in dotted form.
•Label each graph including the dotted line by the corresponding equation and domain and range. Use the textbox for these labels.
Thanks alot for everybody who is willing to help.I dont know how to post a comment that's why I include this to my query This question is from textbook COLLEGE ALGEBRA

Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Can you pls help me
3.)y=x^2-4x
•Graph this original function in its entire domain but coloring green that portion of the graph over the limited domain x>=2,
----
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E2-4x%29
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•Find its inverse over x>=-4,
Inverse? Flip the graph over the line y=x to see the inverse.
This site cannot display it because it is not a function.
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•On another set of coordinate axes, graph this inverse. Color it blue. On this same set of coordinate axis, graph the original f(x)
on the limited domainx>= 2, y>=-4 & color it green.
•Draw the line y = x in dotted form.
•Label each graph including the dotted line by the corresponding equation and domain and range.
=========================
That's the best we can do with this site's graph tools.
Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's graph y=x%5E2-4x


In order to graph y=x%5E2-4x, we need to plot a few points.


To get points in the form of (x,y), we need to find corresponding 'y' values to given 'x' values.


Let's find the y value when x=-2 note: you can start at any x value.


y=x%5E2-4x Start with the given equation.


y=%28-2%29%5E2-4%28-2%29 Plug in x=-2.


y=4-4%28-2%29 Square -2 to get 4


y=4--8 Multiply


y=12 Combine like terms.


So if x=-2, then y=12 which gives us the point (-2,12).


----------------------------


Let's find the y value when x=-1


y=x%5E2-4x Start with the given equation.


y=%28-1%29%5E2-4%28-1%29 Plug in x=-1.


y=1-4%28-1%29 Square -1 to get 1


y=1--4 Multiply


y=5 Combine like terms.


So if x=-1, then y=5 which gives us the point (-1,5).


----------------------------


Let's find the y value when x=0


y=x%5E2-4x Start with the given equation.


y=%280%29%5E2-4%280%29 Plug in x=0.


y=0-4%280%29 Square 0 to get 0


y=0-0 Multiply


y=0 Combine like terms.


So if x=0, then y=0 which gives us the point (0,0).


----------------------------


Let's find the y value when x=1


y=x%5E2-4x Start with the given equation.


y=%281%29%5E2-4%281%29 Plug in x=1.


y=1-4%281%29 Square 1 to get 1


y=1-4 Multiply


y=-3 Combine like terms.


So if x=1, then y=-3 which gives us the point (1,-3).


----------------------------


Let's find the y value when x=2


y=x%5E2-4x Start with the given equation.


y=%282%29%5E2-4%282%29 Plug in x=2.


y=4-4%282%29 Square 2 to get 4


y=4-8 Multiply


y=-4 Combine like terms.


So if x=2, then y=-4 which gives us the point (2,-4).


----------------------------


Let's find the y value when x=3


y=x%5E2-4x Start with the given equation.


y=%283%29%5E2-4%283%29 Plug in x=3.


y=9-4%283%29 Square 3 to get 9


y=9-12 Multiply


y=-3 Combine like terms.


So if x=3, then y=-3 which gives us the point (3,-3).


----------------------------


Let's find the y value when x=4


y=x%5E2-4x Start with the given equation.


y=%284%29%5E2-4%284%29 Plug in x=4.


y=16-4%284%29 Square 4 to get 16


y=16-16 Multiply


y=0 Combine like terms.


So if x=4, then y=0 which gives us the point (4,0).


----------------------------


Let's find the y value when x=5


y=x%5E2-4x Start with the given equation.


y=%285%29%5E2-4%285%29 Plug in x=5.


y=25-4%285%29 Square 5 to get 25


y=25-20 Multiply


y=5 Combine like terms.


So if x=5, then y=5 which gives us the point (5,5).


----------------------------


Let's find the y value when x=6


y=x%5E2-4x Start with the given equation.


y=%286%29%5E2-4%286%29 Plug in x=6.


y=36-4%286%29 Square 6 to get 36


y=36-24 Multiply


y=12 Combine like terms.


So if x=6, then y=12 which gives us the point (6,12).


----------------------------


Now let's make a table of the values we just found.


Table of Values:





xy
-212


-15


00


1-3


2-4


3-3


40


55


612

Now let's plot the points:




Graph:


Now draw a curve through all of the points to graph y=x%5E2-4x:


Graph of y=x%5E2-4x


So the graph of y=x%5E2-4x is




Now shade the graph green from x=2 to the right like so:





To find the inverse, we can do the following...


y=x%5E2-4x Start with the given equation.


x=y%5E2-4y Swap x and y


x=y%5E2-4y%2B4-4 Take half of the y coefficient -4 to get -2. Square -2 to get 4. Add AND subtract this value on the right side.


x=%28y%5E2-4y%2B4%29-4 Group the first three terms.


x=%28y-2%29%5E2-4 Factor that group


x%2B4=%28y-2%29%5E2 Add 4 to both sides.


%28y-2%29%5E2=x%2B4 Rearrange the terms.


y-2=%22%22%2B-sqrt%28x%2B4%29 Take the square root of both sides.


y=2%2B-sqrt%28x%2B4%29 Add 2 to both sides.


y=2%2Bsqrt%28x%2B4%29 or y=2-sqrt%28x%2B4%29 Break up the 'plus/minus'


Now because the directions state that the graph has "the limited domain x>=2", this means that we're only going to focus on the positive portion of the inverse. So we're going to ignore y=2-sqrt%28x%2B4%29.


So the inverse of y=x%5E2-4x (over the domain ) is y=2%2Bsqrt%28x%2B4%29


I'll let you finish up and graph the inverse.