Answer:
Vertical asymptote: 
Horizontal asymptote: 
or x axis.
Step-by-step explanation:
The rational function is given as:
Vertical asymptotes are those values of 
for which the function is undefined or the graph moves towards infinity.
For a rational function, the vertical asymptotes can be determined by equating the denominator equal to zero and finding the values of .
Here, the denominator is 
Setting the denominator equal to zero, we get
Therefore, the vertical asymptote occur at 
.
Horizontal asymptotes are the horizontal lines when tends towards infinity.
For a rational function, if the degree of numerator is less than that of the denominator, then the horizontal asymptote is given as 
.
Here, there is no term in the numerator. So, degree is 0. The degree of the denominator is 3. So, the degree of numerator is less than that of denominator.
Therefore, the horizontal asymptote is at or x axis.
Answer:
Table :
Statements Reasons
1)ΔEGC≅ΔEGB Given
2)EB = EC Corresponding Parts of Congruent
Triangles are Congruent
3) BC = BE Given
4) By 2 and 3 EB≅EC≅BC
5)∠BEC = 60° ΔBEC is an equilateral triangle
Step-by-step explanation:
We are given that BE = BC ---1
We are also given that ΔEGC≅ΔEGB
So, BE = CE(Corresponding Parts of Congruent Triangles are Congruent) ---2
Now By 1 and 2
BE=BC=CE
In ΔBEC
BE=BC=CE
Since all sides are equal . So, it is an equilateral triangle
All angles of equilateral triangle are also equal i.e. 60°
So, ∠BEC = 60°
Hence proved
Table :
Statements Reasons
1)ΔEGC≅ΔEGB Given
2)EB = EC Corresponding Parts of Congruent
Triangles are Congruent
3) BC = BE Given
4) By 2 and 3 EB≅EC≅BC
5)∠BEC = 60° ΔBEC is an equilateral triangle
<h3>
Answer: g(x) = (-2/3)x^2</h3>
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Explanation:
The blue parent function has a positive coefficient of 1. The purple g(x) function is a reflection of f(x) over the x axis, so everything is now negative. The coefficient must be negative as well.
But the answer is simply not g(x) = -x^2 because plugging x = 3 does not lead to y = -6 as the point (3,-6) shows.
Let's say the coefficient is k for now. So we have y = kx^2
Plug in x = 3 and y = -6. Solve for k
y = kx^2
-6 = k(3)^2
-6 = k*9
9k = -6
k = -6/9
k = -2/3
So we update y = kx^2 into y = (-2/3)x^2
Meaning that g(x) = (-2/3)x^2 is the equation of the purple curve.
Plug x = 3 into g(x) to find that
g(x) = (-2/3)x^2
g(3) = (-2/3)(3)^2
g(3) = (-2/3)(9)
g(3) = -6
which is the output we want, so this confirms we have the correct coefficient.
Answer:
3x+2, with a remainder of -6x-4
Step-by-step explanation:
