Objective: Section 3-7 Graphs of Rational Functions 5-Minute Check Lesson 3-7 Objective: Section 3-7 Graphs of Rational Functions

3-7 Graphs of Rational Functions LESSON ESSENTIAL QUESTIONS What is an asymptote (horizontal and vertical) and how do we write it into an equation? How do we graph rational functions and determine the asymptotes? Objective: Section 3-7 Graphs of Rational Functions

Objective: Section 3-7 Graphs of Rational Functions What you will learn 1. How to graph a rational function based on the parent graph. 2. How to find the horizontal, vertical and slant asymptotes for a rational function. Objective: Section 3-7 Graphs of Rational Functions

Yeah! Definitions 1. Rational Function: A quotient of two polynomial functions. 2. Asymptote: A line that a graph approaches but never intersects. (Can be horizontal, vertical, or slant) Objective: Section 3-7 Graphs of Rational Functions

Types of Asymptotes Horizontal asymptote: the line y = b is a horizontal asymptote for a function f(x) if f(x) approaches b as x approaches infinity or as x approaches negative infinity. Vertical asymptote: the line x = a is a vertical asymptote for a function f(x) if f(x) approaches infinity or f(x) approaches negative infinity as x approaches “a” from either the left or the right. Slant asymptote: the oblique line “l” is a slant asymptote for a function f(x) if the graph of y = f(x) approaches “l” as x approaches infinity or as x approaches negative infinity. Objective: Section 3-7 Graphs of Rational Functions

Visual Vocabulary Vertical asymptote Horizontal Asymptote Objective: Section 3-7 Graphs of Rational Functions

Slant Asymptote Slant Asymptote Objective: Section 3-7 Graphs of Rational Functions

Finding Asymptotes Find the asymptotes for the graph of Vertical asymptote: value of x that causes a “0” in the denominator. x – 2 = 0 x = 2 is vert. as. Check: X F(x) 1.9 1.99 1.999 1.9999 Objective: Section 3-7 Graphs of Rational Functions

Finding Asymptotes (cont.) Find the asymptotes for the graph of Horizontal asymptotes: Divide the numerator and the denominator by the highest power of x. Ask yourself, as x gets infinitely large, what would the value of the function be? Objective: Section 3-7 Graphs of Rational Functions

You Try Determine the asymptotes for the graph of: Objective: Section 3-7 Graphs of Rational Functions

Finding Slant Asymptotes Slant asymptotes occur when the degree of the numerator of a rational function is exactly one greater than the degree of the denominator. Example: Find the slant asymptote for: Objective: Section 3-7 Graphs of Rational Functions

You Try Find the slant asymptote for: Objective: Section 3-7 Graphs of Rational Functions

Graphing Rational Functions Can you predict what will happen as we graph the following: 1. 2. 3. 4. Objective: Section 3-7 Graphs of Rational Functions

Let’s See Objective: Section 3-7 Graphs of Rational Functions

How About… Objective: Section 3-7 Graphs of Rational Functions

How About… Objective: Section 3-7 Graphs of Rational Functions

How About Objective: Section 3-7 Graphs of Rational Functions