as x 2- (from the left), f(x) → → ∞ as x f(x) 0+ → ∞, → as x - f(x) 0- → ∞, → Sketch at least two graphs of a rational function satisfying the following conditions The vertical asymptote is x = 2 The horizontal asymptote is y = 1 Graph 1 Graph 2 Now for each of the graphs complete the following: For Graph 1 For 1 As x 2+ then y As x 2+ then y → →…….. → →…….. As x 2- then y As x 2- then y → →…….. → →…….. As x then y As x then y → ∞ →…….. → ∞ →…….. As x -∞ then y As x -∞ then y → →…….. → →…….. Sketch the graph of a rational function satisfying the following conditions The x-intercepts are and 2 –2 The vertical asymptote is x = 0 The horizontal asymptote is y = -5 Now complete the following: As x 0+ then y → →…….. As x 0- then y → →…….. As x then y → ∞ →…….. As x -∞ then y → →…….. Math 165 - Sections 4.4 and 4.5 Rational Functions – Write the equation of a rational function that satisfies the following conditions: x = 5 is the vertical asymptote y = 0 is the horizontal asymptote
as x → 2- (from the left), f(x) → ∞ as x → ∞, f(x) → 0+ as x → - ∞, f(x) → 0- Sketch at least two graphs of a rational function satisfying the following conditions The vertical asymptote is x = 2 The horizontal asymptote is y = 1 Graph 1 Graph 2 Now for each of the graphs complete the following: For Graph 1 As x → 2+ then y →…….. As x → 2- then y →…….. As x → ∞ then y →…….. As x → -∞ then y →…….. For 1 As x → 2+ then y →…….. As x → 2- then y →…….. As x → ∞ then y →…….. As x → -∞ then y →…….. Sketch the graph of a rational function satisfying the following conditions The x-intercepts are –2 and 2 The vertical asymptote is x = 0 The horizontal asymptote is y = -5 Now complete the following: As x → 0+ then y →…….. As x → 0- then y →…….. As x → ∞ then y →…….. As x → -∞ then y →…….. Math 165 - Sections 4.4 and 4.5 – Rational Functions Write the equation of a rational function that satisfies the following conditions: x = 5 is the vertical asymptote y = 0 is the horizontal asymptote
Sections4.4-5-in-class.docx