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Pre-Calculus

Pre-Calculus. Chapter 1 Functions and Their Graphs. 1.2.2 Functions & Applications. Objectives: Use piecewise-defined functions. Use functions to model and solve real-life problems. Warm Up 1.2.2.

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Pre-Calculus

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  1. Pre-Calculus Chapter 1 Functions and Their Graphs

  2. 1.2.2 Functions & Applications • Objectives: • Use piecewise-defined functions. • Use functions to model and solve real-life problems.

  3. Warm Up 1.2.2 • The dollar value of a VCR in 2004 is $85, and the product will decrease in value at an expected rate of $10.75 per year. • Write a linear equation that gives the dollar value V of the VCR in terms of the year t. (Let t = 4 represent the year 2004.) • Estimate the dollar value of the VCR in 2008.

  4. Vocabulary • Piecewise-Defined Function • Absolute Value Function • Square Root Function

  5. Example 1 • The number N (in millions) of cell phone users in the U.S. increased in a linear pattern from 1995 to 1997. Then, in 1998, the number of users took a jump, and until 2001, increased in a different linear pattern. These patterns can be approximated by the function where t represents the year, t = 5 corresponding to 1995. Approximate the number of cell phone users for each year from 1995 to 2001.

  6. Piecewise-Defined Function • Piecewise-defined function A function defined by two or more equations over a specified domain. The absolute value function can be written as a piecewise-defined function.

  7. Absolute Value Function

  8. Warm Up Day 2 • A baseball is hit at a point 3 feet above the ground at a velocity of 100 feet per second and an angle of 45°. The path of the ball is given by the function f (x) = –0.0032x2 + x + 3 where y and x are measured in feet. Will the ball clear a 10-foot fence located 300 feet from home plate?

  9. Square Root Function

  10. Example 2 • Find the domain of the function.

  11. Example 3 • Use your graphing calculator to find the domain and range of each function. • f (x) = │x + 2│ b.

  12. Summary of Function Terminology 1 • Function A relationship between two variables such that to each value of the independent variable there corresponds exactly one value of the dependent variable.

  13. Summary of Function Terminology 2 • Function Notation: y = f (x) f is the name of the function. y is the dependent variable. x is the independent variable. f (x) is the value of the function at x.

  14. Summary of Function Terminology 3 • Domain The set of all values (inputs) of the independent variable for which the function is defined. • If … Then … • x is in the domain of ff is defined at x • xis not in the domain of ff is undefined at x.

  15. Summary of Function Terminology 4 • Range: The set of all values (outputs) assumed by the dependent variable (that is, the set of all function values). • Implied Domain: If f is defined by an algebraic expression and the domain is not specified, the implied domain consists of all real numbers for which the expression is defined.

  16. Homework 1.2.2 • Worksheet 1.2.2 • # 39 – 61 odd, 74, 79, 95 – 98 all

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