How to find the end behavior of a rational function

Asked by admin @ 05/11/2021 in Mathematics viewed by 294 People

State the domain and end behavior of each rational function. Identify all horizontal and vertical asymptotes on the

graph of each rational function. Then, verify your answer by graphing the function on the graphing calculator.
1. f(x) = −x + 6 / 2x + 3
2. f(x) = 3x − 6 / x
3. f(x) = 3 / x2 − 25
4. f(x) = x2 − 2 / x2 + 2x − 3
5. f(x) = x2 − 5x − 4 / x + 1
6. f(x) = 5x / x2 + 9

Answered by admin @ 05/11/2021

Answer:

Rational Functions

Step-by-step explanation:

$f(x) = - \frac{x + 6}{2x + 3}$

• State the domain

X ∈ R : $x \neq - \frac{3}{2}$

• End Behaviour

$x \rightarrow \infty , y \rightarrow -\frac{1}{2}$

• Horizontal and Vertical

$y= -\frac{1}{2} , x=-\frac{3}{2}$

• Graphic (Annex)

2) $f(x) = \frac{3x − 6}{x}$

• State the domain

X ∈ R : $x \neq 0$

• End Behaviour

$x \rightarrow \infty , y \rightarrow 3$

• Horizontal and Vertical

$y= 0$

• Graphic (Annex)

3) $f(x) = \frac{3}{x^2-25}$

• State the domain

X ∈ R : $x \neq 5.5$

• End Behaviour

$x \rightarrow +/-\infty , y \rightarrow 0$

• Horizontal and Vertical

$y= 0 , x=+/- 5$

• Graphic (Annex)

4) $f(x) = \frac{ x^2-2}{x^2+2x-3}$

• State the domain

X ∈ R : $x \neq (3,1)$

• End Behaviour

$x \rightarrow +/-\infty , y \rightarrow +/- 1$

• Horizontal and Vertical

$y= 1 , x= (-3,1)$

• Graphic (Annex)

5) $f(x) = \frac{ x^2 − 5x − 4}{x + 1}$

• State the domain

X ∈ R : $x \neq -1$

• End Behaviour

$x \rightarrow +/-\infty , y \rightarrow +/ \infty$

• Horizontal and Vertical

$y=none , x= -1$

• Graphic (Annex)

6) $f(x) = \frac{ 5x }{x^2 + 9 }$

• State the domain

X ∈ R

• End Behaviour

$x \rightarrow +/-\infty , y \rightarrow 0$

• Horizontal and Vertical

$y= 0 , x= none$

• Graphic (Annex)

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