Unit 1 ­ Rational Functions and Polynomial Expressions.notebook
February 26, 2014
Review
Before the break we looked at: ­ simplifying rational expressions
­ operations (+, ­, x, ÷) with rational expressions
­ solving rational equations
Let's brush up with a few examples: x
Jan 18­10:34 AM
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Unit 1 ­ Rational Functions and Polynomial Expressions.notebook
February 26, 2014
Example
The Greek mathematician Pythagoras is credited with discovering the golden rectangle. This is considered to be the rectangle with the most visually appealing dimensions. In a golden rectangle, the length, l, and the width, w, are related by the following equation: A billboard with a length of 15 m is being designed. If the designers want the billboard to be a golden rectangle, what must its width be? Jan 18­10:34 AM
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Unit 1 ­ Rational Functions and Polynomial Expressions.notebook
February 26, 2014
Example
Rima bought a case of concert t­shirts for $450. She kept two shirts for herself and sold the rest for $560, making a profit of $10 on each shirt. How many t­shirts were in the case? Jan 18­10:34 AM
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Unit 1 ­ Rational Functions and Polynomial Expressions.notebook
February 26, 2014
A golf­course designer travels 2520 km in a corporate jet and then an additional 420 km by car in order to arrive at a particular project site. The speed of a jet is 8 times the speed of the car. Molly must obtain an average mark of 50% to pass her math course. There are 6 equally weighted tests in the course, and Molly received 50% on four of the five tests and 52% on one of the tests. If the car ride takes 1h longer than the ride in the jet, then how much time does the designer spend travelling by car? What is the minimum mark that Molly must achieve on her sixth test in order to pass the course? A. 3 h
B. 3.5 h
C. 3.75 h
D. 4 h
A. 41%
B. 45%
C. 48%
D. 51%
Jan 18­10:34 AM
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Unit 1 ­ Rational Functions and Polynomial Expressions.notebook
February 26, 2014
Homework
page 259­260 # 9­18
Challenge yourself! Do # 19 and 20 too! Jan 18­10:34 AM
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Unit 1 ­ Rational Functions and Polynomial Expressions.notebook
February 26, 2014
Objective
Identify characteristics of the graphs of polynomial functions. Jan 18­10:34 AM
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Unit 1 ­ Rational Functions and Polynomial Expressions.notebook
February 26, 2014
Definition
What is a polynomial? What makes it a polynomial? A polynomial is an expression of algebraic terms that contain different powers of the same variable. The expression can have constants, variables and exponents, but the exponents can only be greater than or equal to 0. Jan 18­10:34 AM
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Unit 1 ­ Rational Functions and Polynomial Expressions.notebook
February 26, 2014
Properties of Polynomial Graphs
Polynomials have been studied for centuries, partly because of their simplicity, because they only contain multiplication and addition. We're going to begin our study of polynomials by looking at the following characteristics of their graphs: • the number of x­intercepts
• the y­intercept
• the end behaviour
• the domain
• the range
Jan 18­10:34 AM
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Unit 1 ­ Rational Functions and Polynomial Expressions.notebook
February 26, 2014
Linear Functions
Examples of Linear Functions:
For the linear functions you graphed, what was: • the number of x­intercepts
• the y­intercept
• the end behaviour
• the domain
• the range
Jan 18­10:34 AM
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Unit 1 ­ Rational Functions and Polynomial Expressions.notebook
February 26, 2014
Linear Functions
Examples of Quadratic Functions:
For the quadratic functions you graphed, what was: • the number of x­intercepts
• the y­intercept
• the end behaviour
• the domain
• the range
Jan 18­10:34 AM
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