Question

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

Answer 1

Answer:

Rational Functions

Step-by-step explanation:

1)

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

• 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)