Pre-Calculus/Trig Name: _________________________
UNIT 1: Algebra II Review – SECTION 7 WORKSHEET #1 Date: _________________________
GRAPHING RATIONAL FUNCTIONS
To Identify Types of Discontinuity:
Step 1: HOLES (Removable Discontinuities)
✓ Factor numerator & denominator
✓ Simplify
✓ If anything cancels, then there is a hole (More than one factor cancels More than one hole)
✓ Find the ordered pair, (𝑥, 𝑦), substitute x into the SIMPLIFIED EQUATION to get y
Step 2: VERTICAL ASYMPTOTES (USE SIMPLIFIED EQUATION)
✓ Set simplified equation denominator = 0, solve for x
Step 3: HORIZONTAL ASYMPTOTES – Two Cases (USE SIMPLIFIED EQUATION)
✓ Degree of Denominator = Degree of Numerator 𝑦 = ratio of leading coefficients
✓ Degree of Denominator > Degree of Numerator 𝑦 = 0
Step 4: SLANT ASYMPTOTES (Exists only if Horizontal Asymptote is not present) (USE SIMPLIFIED EQUATION)
✓ Degree of Numerator is ONE degree larger than the Degree of Denominator
✓ Use Long Division
✓ Ignore the remainder
✓ Answer in the form 𝑦 = 𝑚𝑥 + 𝑏
Directions: State each discontinuity, 𝑥-intercept, and 𝑦-intercept. Then sketch a graph.
1.) 𝑓(𝑥)=𝑥2−4
𝑥−2
HOLE(S)
VERTICAL
ASYMPTOTE(S)
HORIZONTAL
ASYMPTOTE
SLANT
ASYMPTOTE
𝒙-intercept(s)
𝒚-intercept
