Rational Functions Characteristics

The graph is a reflection of the parent funtion $$y=\frac{1}{x}$$

An equation for the function is $$y=\frac{-1}{x-1}$$

There is a vertical asymptote at

$$x=-1$$

There is a horizontal asymptote at $$y=0$$

The domain is $$\left(-\infty,\ -8\right)\cup\ \left(-8,\ \infty\right)$$

The range is $$\left(-\infty,\ 6\right)\cup\ \left(6,\ \infty\right)$$

The graph is stetched vertically

There is a vertical asymptote at $$x=8$$

a = 1

h = -1

k = 2

$$y=\frac{1}{x+1}+2$$

The graph has been shifted up 2 from the parent function

The range is $$\left(-\infty,\ -1\right)\cup\ \left(-1,\ \infty\right)$$

There is a vertical asymptote at $$x=3$$

a = -2

h = -3

k = -1

The range is $$\left(-\infty,\ -1\right)\cup\ \left(-1,\ \infty\right)$$

A hole occurs where x=3

vertical asymptote at x=3

vertical asymptote at x=5

A hole occurs where x=5

there is no horizontal asymptote

the exponents in the numerator and denominator are equal

the exponents in the denominator are greater than the numerator

the exponents in the numerator are greater than the denominator

the numerator equals zero

A hole occurs where x=3

vertical asymptote at x=3

vertical asymptote at x=5

A hole occurs where x=5

The function is discontinuous at x={-5, -3}

y = -2

y = 0

y = 1/2

x = 2

$$x\ne2$$  

none