Answer: Horizontal asymptote is
and vertical asymptotes are ![\pm \dfrac{1}{2i}](https://tex.z-dn.net/?f=%5Cpm%20%5Cdfrac%7B1%7D%7B2i%7D)
Step-by-step explanation:
Since we have given that
![y=\dfrac{x^2-9}{4x^2+1}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7Bx%5E2-9%7D%7B4x%5E2%2B1%7D)
We need to find the horizontal and vertical asymptotes.
Since vertical asymptotes will occur where the denominator becomes zero.
So, here denominator is ![4x^2+1](https://tex.z-dn.net/?f=4x%5E2%2B1)
Now,
![4x^2+1=0\\\\4x^2=-1\\\\x^2=\dfrac{-1}{4}\\\\x=\pm \dfrac{1}{2i}](https://tex.z-dn.net/?f=4x%5E2%2B1%3D0%5C%5C%5C%5C4x%5E2%3D-1%5C%5C%5C%5Cx%5E2%3D%5Cdfrac%7B-1%7D%7B4%7D%5C%5C%5C%5Cx%3D%5Cpm%20%5Cdfrac%7B1%7D%7B2i%7D)
And the horizontal asympototes will occur when the coefficient of higher degree of numerator is divided by coefficient of higher degree of denominator.
![y=\dfrac{1}{4}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B1%7D%7B4%7D)
Hence, horizontal asymptote is
and vertical asymptotes are ![\pm \dfrac{1}{2i}](https://tex.z-dn.net/?f=%5Cpm%20%5Cdfrac%7B1%7D%7B2i%7D)
Answer:
x=8
Step-by-step explanation:
Answer:
-3.392
Step-by-step explanation:
2.34
1.052
+_____
= 3.392
Answer:
p = q
Step-by-step explanation:
Angles in a triangle add up to 180°
For the left triangle:
180 = p + 20 + 80
p = 80
For the right triangle:
180 = q + 45 + 55
q = 80
Therefore, p = q
To reflect a function across the y-axis you have to change
![x\mapsto -x](https://tex.z-dn.net/?f=x%5Cmapsto%20-x)
So, the function becomes
![f(x)=-2x^2+5x-3 \mapsto f(-x)=-2(-x)^2+5(-x)-3=-2x^2-5-3](https://tex.z-dn.net/?f=f%28x%29%3D-2x%5E2%2B5x-3%20%5Cmapsto%20f%28-x%29%3D-2%28-x%29%5E2%2B5%28-x%29-3%3D-2x%5E2-5-3)