Rational Functions Vertical Asymptotes Holes and Graphs

Identify any Vertical Asymptotes for this rational function h\left(x\right) \ =\ \frac{x+2}{4-x^2}

• x  =  2

• x  =  +/- 2

• (2, 0)

• y = 2

Identify any removable discontinuities (holes) in this rational function:

• No holes

• Hole at (2, 0) and (-3, 0)

• Hole at x = - 2

• Hole at (-2,0)

Identity any removable discontinuities (holes) in this rational function...

• hole at (-1/3, 1/3)

• no hole

• hole at (-1/3, 0)

• hole at (-1/3, -2)

What are the x - intercepts of this rational function?

• (0, 1)

• (1, 0)

• -1, and 1

• 1, - 1, and 0

Identify any Vertical Asymptotes for this rational function

• There are none

• x = 2

• x = +/- 2

• x = 0, and x = - 2

What is the y - intercept of this rational function?

• (0, 2)

• (-2, 0)

• There are two:  y = +/- 2

• (0, -2)

What is the y - intercept of this rational function?

• (4/3, 0) ... (1, 0) is not in domain of function

• (4, 0)

• (0, 4)

• (0, -4)

Which of the following could be the equation of f(x)? (Hint: Focus on the hole, zero, and vertical asymptote.)

Which of the following could be the equation of f(x)? (Hint: Focus on the hole, zero, and vertical asymptote.)

How do you find the end behavior?

• Set the simplified denominator equal to zero.

• Set the canceled out parts of the denominator equal to zero.

• Set the simplified numerator equal to zero.

• Use the leading terms of the numerator and denominator.