SOLUTION: Please help.
1.) What is the end behavior of the graph of y=-1.5x^4+3x^2-4x-4
2. Determine all x-intercepts of the rational function f(x)=x^2-2x/(x+4)^2
3. Find the x-coor
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Question 64294: Please help.
1.) What is the end behavior of the graph of y=-1.5x^4+3x^2-4x-4
2. Determine all x-intercepts of the rational function f(x)=x^2-2x/(x+4)^2
3. Find the x-coordinates of the points of intersection between two functions x^2+y^2=113 and x+y=-15
4. Give the equation of a line that passes through the point (7,4) and is perpendicular to the line whose equation is given by 4x+5y=8
Thank you!!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1.) What is the end behavior of the graph of y=-1.5x^4+3x^2-4x-4
"End behavior" asks what happens to y as x gets arbitrarily large
is a positive and in a negative direction. The highest power term
determines what happens.
As x gets very positively large -1.5x^4 gets very negative so the
end behavior is: as x goes to infinity, y goes to negative infinity.
As x gets very negatively large -1.5x^4 gets very negative so the
end behavior is : as x goes to negative infinity, y goes to negative
infinity.
----------------
2. Determine all x-intercepts of the rational function f(x)=x^2-2x/(x+4)^2
Let y= 0 and solve for x:
0=[(x^2-2x)/x+4)^2]
This fraction will be 0 when the numerator is 0.
x^2-2x=0
x(x-2)=0
x=0 or x=2 (they are the x-intercepts)
------------
3. Find the x-coordinates of the points of intersection between two functions x^2+y^2=113 and x+y=-15
If x+y=-15 y=-x-15
The line touches the circle at (-7,-8)
-------------------
4. Give the equation of a line that passes through the point (7,4) and is perpendicular to the line whose equation is given by 4x+5y=8
The give line has a slope of (-4/5).
The line perpendicular to it will have a slope of 5/4.
The form of the line is y=mx+b; you have x=7, y=4, m=5/4; you need "b":
4=(5/4)7+b
4=35/4 + b
b=16/4 - 35/4
b=-19/4
EQUATION:
y=(5/4)x-(19/4)
--------------
Cheers,
Stan H.
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