i) The given function is
![f(x)=\frac{x-5}{2x^2-5x-3}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7Bx-5%7D%7B2x%5E2-5x-3%7D)
The factored form is
![f(x)=\frac{x-5}{(x-3)(2x+1)}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7Bx-5%7D%7B%28x-3%29%282x%2B1%29%7D)
The domain are the values of x for which the function is defined.
![(x-3)(2x+1)\ne 0](https://tex.z-dn.net/?f=%28x-3%29%282x%2B1%29%5Cne%200)
![(x-3)\ne0,(2x+1)\ne 0](https://tex.z-dn.net/?f=%28x-3%29%5Cne0%2C%282x%2B1%29%5Cne%200)
![x\ne3,x\ne-\frac{1}{2}](https://tex.z-dn.net/?f=x%5Cne3%2Cx%5Cne-%5Cfrac%7B1%7D%7B2%7D)
ii) To find the vertical asymptotes, equate the denominator to zero.
![(x-3)(2x+1)=0](https://tex.z-dn.net/?f=%28x-3%29%282x%2B1%29%3D0)
![(x-3)=\ne0,(2x+1)=0](https://tex.z-dn.net/?f=%28x-3%29%3D%5Cne0%2C%282x%2B1%29%3D0)
![x=3,x=-\frac{1}{2}](https://tex.z-dn.net/?f=x%3D3%2Cx%3D-%5Cfrac%7B1%7D%7B2%7D)
iii) To find the roots, equate the numerator to zero.
![x-5=0](https://tex.z-dn.net/?f=x-5%3D0)
The root is ![x=5](https://tex.z-dn.net/?f=x%3D5)
iv) To find the y-intercept, put
into the function.
![f(0)=\frac{0-5}{(0-3)(2(0)+1)}](https://tex.z-dn.net/?f=f%280%29%3D%5Cfrac%7B0-5%7D%7B%280-3%29%282%280%29%2B1%29%7D)
![f(0)=\frac{-5}{(-3)(1)}](https://tex.z-dn.net/?f=f%280%29%3D%5Cfrac%7B-5%7D%7B%28-3%29%281%29%7D)
![f(0)=\frac{5}{3}](https://tex.z-dn.net/?f=f%280%29%3D%5Cfrac%7B5%7D%7B3%7D)
The y-intercept is ![\frac{5}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B3%7D)
v) The horizontal asymptote is given by;
![lim_{x\to \infty}\frac{x-5}{2x^2-5x-3}=0](https://tex.z-dn.net/?f=lim_%7Bx%5Cto%20%5Cinfty%7D%5Cfrac%7Bx-5%7D%7B2x%5E2-5x-3%7D%3D0)
The horizontal asymptote is ![y=0](https://tex.z-dn.net/?f=y%3D0)
vi) The function is not reducible. There are no holes.
vii) The given function is a proper rational function.
Proper rational functions do not have oblique asymptotes.
Answer:
d) The government reduces public transportation costs by switching to propane-run buses without adjusting taxes.
Step-by-step explanation:
The correct choice among the given 4 which could result in a county government budget in surplus is,
d) The government reduces public transportation costs by switching to propane-run buses without adjusting taxes.
Answer:
Dec 7, 2020 — Calculate the ratio of the lengths of the two line segments formed on each transversal. You will have two sets of calculations. Round your ... sets of calculations. Round your answers to the hundredths place. What do you notice about the ratios of the lengths for each transversal? How do they compare? 1.
Step-by-step explanation:
brainlist please or else ill kill you understand
You need to distribute the 4, so you'll end up with:
4n-16=-12
Then, add 16 to both sides.
4n-16+16=-12+16
4n=4
Divide by 4 on both sides.
4/4n=4/4
n=1