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Section 2.1 What is a function?

Section 2.1 What is a function?. Objectives: To understand functions and function notation. To review domain. To understand how to evaluate functions and piecewise functions. To understand the difference quotient. Functions.

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Section 2.1 What is a function?

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  1. Section 2.1What is a function? Objectives: To understand functions and function notation. To review domain. To understand how to evaluate functions and piecewise functions. To understand the difference quotient.

  2. Functions • A curve in the coordinate plane is the graph of a function if and only if no vertical line intersects the curve more than once. • Vertical Line Test – when given a graph, use this to verify if the curve is a function

  3. Ex 1. Use the vertical line test to determine if the following graphs are functions.

  4. Functions A function is a relationship between two variables such that each value of the first variable is paired with exactly one value of the second variable. Function notation: f(x) = y f(2) means evaluate the given function when x=2

  5. Ex 2. Given • Evaluate: • f(3) • f(-2) • f( )

  6. Getting Information from a Graph • The values of a function are represented by the height of its graph above the x-axis. • So, we can read off the values of a function from its graph.

  7. Ex. 3 Find the Values of a Function from a Graph The function T graphed here gives the temperature between noon and 6 P.M. at a certain weather station. • Find T(1), T(3), and T(5). • Which is larger, T(2) or T(4)?

  8. Class Work 1) a) Find f(50). b) Find f(100).

  9. Class Work 2.) Evaluate at the given values. • f(-2) b) f(4) c) f( ½ )

  10. Piecewise Functions A piecewise function is defined by different formulas on different parts of the domain.

  11. Ex 4. A cell phone plan costs $39 a month. • The plan includes 400 free minutes and charges 20¢ for each additional minute. • The monthly charges are a function of the number of minutes used, given by • Find C(100), C(400), and C(480)

  12. Class Work • Evaluate the piecewise functions at the indicated values. • f(-5) • f(3) • f(0) • f(1)

  13. Difference Quotient Ex 4. Evaluate f(x) = 3x – 1 at the following values. • f(a) • f(a + h)

  14. Class Work • Find the difference quotient, for the function:

  15. Use the function to evaluate the indicated expression and simplify. f(x) = 3x – 1 • f(2x) = • 2f(x) = • f(x2) = • (f(x))2=

  16. Pg.155 (13-27) odd, 29, 31, 35, 59, 60, 67, 68Pg. 167 (23-26, 55-60) all

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