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Complete:
The equation f(X)=P(x)Q(x),Q(X)≠0f(X)=\frac{P\left(x\right)}{Q\left(x\right)},Q(X)\ne0f(X)=Q(x)P(x),Q(X)=0 is the form of the ________ .
Rational function
Identity function
Empty function
Every rational function has at most one ________.
Horizental asymptote
Vertical asymptote
None of these
Which of the following is a rational function?
f(x)=x2+5f(x)=x^2+5f(x)=x2+5
f(x)=x−32\ f(x)=\frac{x-3}{2} f(x)=2x−3
Write ratioanl function of this equation
(4x+1)−(3x−1)\left(\frac{4}{x+1}\right)-\left(\frac{3}{x-1}\right)(x+14)−(x−13)
−2〖x2−1)\frac{-2}{〖x^2-1)}〖x2−1)−2
−1〖x2−1)\frac{-1}{〖x^2-1)}〖x2−1)−1
−2〖x2+1)\frac{-2}{〖x^2+1)}〖x2+1)−2
f(x)=x2+12\ f(x)=\frac{x^2+1}{2} f(x)=2x2+1
f(x)=xf(x)=xf(x)=x
f(x)=2x−1f(x)=2x-1f(x)=2x−1
f(x)=3x+1x2−4\ f(x)=\frac{3x+1}{x^2-4} f(x)=x2−43x+1
These are functions in the formf(x)=g(x)h(x) where h(x)≠0.f\left(x\right)=\frac{g\left(x\right)}{h\left(x\right)}\ where\ h\left(x\right)\ne0.f(x)=h(x)g(x) where h(x)=0.
Linear functions
Rational functions
f(x)=x2+1f\left(x\right)=x^2+1f(x)=x2+1
f(x)=1x\ f(x)=\frac{1}{x} f(x)=x1
f(x)=2x2−4f(x)=2x^2-4f(x)=2x2−4
f(x)=x2x−4\ f(x)=\frac{x^2}{x-4} f(x)=x−4x2
f(x)=2−xx−1\ f(x)=\frac{2-x}{x-1} f(x)=x−12−x
f(x)=3x2f(x)=3x^2f(x)=3x2
It is done.