5.3 Graphing Rationa Functions

What are the types of discontinuities (select all that apply)?

(HINT: Check your notes)

• holes (removeable)

• asymptotes (non-removeable)

• irrational

• continuous on the domain

Find and classify each discontinuity of the function.

 $f\left(x\right)=\frac{x}{x+5}$  

• x = 5, vertical asympotoe 

• x = -5, hole 

• x = -5, vertical asymptote

• continuous on the domain

Find and classify the discontinuity of the function.

 $f\left(x\right)=\frac{1}{x^2+9}$  

• x=3, x=-3, vertical asymptotes

• x=3, x=-3, hole

• x=3, hole
  x=-3, vertical asymptotes

• continuous on the domain

What should you be looking for when trying to determine the domain of the function? (Select all that apply)

• even radicals can't be negative.

• the value of the input can't be greater than the value of the output.

• cannot divide by zero.

• domain can't contain fractions.

What is the equation of the horizontal asymptote?

• y = 0

• y = -2

• y = 2

• There isn't one

What is the equation of the vertical asymptote?

• x = 0

• x = 4

• x = -1, x = 4

• x = -1

What are the coordinates of the hole, if one exists.

• (-1, -2)

• (-1, ½)

• (-1, -½)

• there isn't one

What is the domain?

• x ≠ 3

• x ≠ -1

• x ≠ 3, -1

• x ≠ 3, 1

What are the x and y intercepts?

• (4, 0) and (0, -4)

• (-4, 0) and (0, -4)

• (-4, 0) and (0, 4)

• (0, 0) and (0, -4)

Which statements are true for the given rational function. Select all that apply.

• The horizontal asymptote is at y = 0.

• There is a hole at (6, ¾ ).

• The vertical asymptote is at x = -2.

• The x and y intercepts are at the origin.

• The domain is all real numbers except -2.