Graphing more challenging Rational Functions

Warm-Up 1. a) 0 11 = b) 8 0 = Evaluate when x = 0 2. a) 𝑥−15 𝑥−3 = b) 𝑥 2 +2𝑥+8 𝑥 2 −𝑥 −2 = Solve. 3. a) x2 + 36 = 0 b) x2 + 2x – 35 = 0 4. a) 0 = 5𝑥+30 𝑥 −2 b) 0 = 2𝑥 2 −18 3 𝑥 2

Label the asymptotes and intercepts.

Rules for horizontal asymptotes If a rational function is in the form y = 𝑎 𝑥 𝑚 + …. 𝑏 𝑥 𝑛 +… then: if m>n there is no horizontal asymptote if m = n, then y = 𝑎 𝑏 is the equation for the asymptote if m < n, then y = 0 is the equation for the horizontal asymptote

Steps in graphing rational functions Find vertical asymptotes (where the bottom equals zero) Find the horizontal asymptotes using the 3 rules you learned Find the y-intercept (where x is zero) Find the x-intercept(s) (where y is zero) Plot a couple of points between each set of vertical asymptotes.

𝑦= 2𝑥 𝑥−3

y = 2𝑥+12 𝑥 2 −4

y = 𝑋 2 −𝑋−6 𝑋 2 −𝑋−2