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A. Find the domain and range of the following rational functions. Item no.1 is done for you.

1.(x)= 3/x-5 Domain: D(f):{x E R|x≠5} Range:D(f): {Y E R|y ≠0}

2. (x)=2-3x/x+1 Domain: Range:

3.(x)=2-x/x-3 Domain: Range:

4.(x)=x-8/4x+2 Domain: Range:​

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FREDMALONZO1969GO

Answer:

The domain is x∈(−∞,−1)∪(−1,1)∪(1,∞).

The range is y∈R .

Explanation:

As you cannot divide by

0 , the denominator is ≠0

Therefore,

x2−1≠0

⇒ , (x−1)(x+1)≠0

So, x≠1 and x≠−1

The domain is

x∈(−∞,−1)∪(−1,1)∪(1,∞)

To calculate the range, let

y=3xx2−1

⇒ , y(x2−1)=3x

⇒ , yx2-y=3x

⇒ . yx2−3x−y=0

This ia a quadratic equation in x

and in order to have solutions, the discriminant must be ≥0

Therefore,

Δ=(−3)2−4(y)(−y)≥0

9+4y2≥0

So,

∀y∈R , 9+4y2≥0

The range is

y∈R

graph{3x/(x^2-1) [-18.02, 18.02, -9.01, 9.02]}

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