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1.2 Functions

1.2 Functions . Determine whether relations between two variables represent functions Use function notation and evaluate functions Find the domains of functions Use functions to model and solve real-life problems Evaluate difference quotients. Definition of a Function:.

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1.2 Functions

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  1. 1.2 Functions • Determine whether relations between two variables represent functions • Use function notation and evaluate functions • Find the domains of functions • Use functions to model and solve real-life problems • Evaluate difference quotients

  2. Definition of a Function: A function is a relation in which each element of the domain (the set of x-values, or input) is mapped to one and only one element of the range (the set of y-values, or output). Function Not a Function One-to-one Function

  3. A Function can be represented several ways: • Verbally – by a sentence that states how the input is related to the output. • Numerically – in the form of a table or a list of ordered pairs. • Graphically – a set of points graphed on the x-y coordinate plane. • Algebraically – by an equation in two variables.

  4. Example 1

  5. Example 2 Which of the equations represents y as a function of x? a. b.

  6. Example 3Let g(2)= g(t)= g(x+2)=

  7. Example 4 : Evaluate the piecewise function when x=-1 and x=0.

  8. Example 5 : Find the domain of each function • f: {(-3,0),(-1,4),(0,2),(2,2),(4,-1)} b. c. d. e.

  9. Example 6 Use a graphing calculator to find the domain and range of the function

  10. Example 7 The number N (in millions) of cellular phone subscribers in the United States increased in a linear pattern from 1995 to 1997, as shown on p.22. Then, in 1998, the number of subscribers took a jump, and until 2001, increased in a different linear pattern. These two patterns can be approximated by the function where t represents the year, with t=5 corresponding to 1995. Use this function to approximate the number of cellular phone subscribers for each year from 1995 to 2001.

  11. Example 8 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 degrees. The path of the baseball is given by the function where y and x are measured in feet. Will the baseball clear a 10 foot fence located 300 feet from home plate?

  12. Student Example A baseball is hit at a point 4 feet above the ground at a velocity of 120 feet per second and an angle of 45 degrees. The path of the baseball is given by the function where y and x are measured in feet. Will the baseball clear an 8 foot fence located 350 feet from home plate?

  13. Example 9 For .

  14. Student Example Evaluate for f(-3) f(x+1) f(x+h)-f(x)

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