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1.4 Analyzing Graphs of Functions

1.4 Analyzing Graphs of Functions. Testing for even and odd functions. Interval Notation . When the end points are included [ ]. When the end points are not included ( ). (4,8) Domain from (2, -3) to (5, -1) Written as [2, 5) Range [ -3, 8]

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1.4 Analyzing Graphs of Functions

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  1. 1.4 Analyzing Graphs of Functions Testing for even and odd functions

  2. Interval Notation When the end points are included [ ]. When the end points are not included ( ). (4,8) Domain from (2, -3) to (5, -1) Written as [2, 5) Range [ -3, 8] open and close becomes a big deal (2, -3) (5,-1)

  3. Testing for a function Graphically using the Vertical line test. “ A set of points in a coordinate plane is the graph of y as a function of x iff no vertical line intersect the graph at more than one point.” Not a Function Function

  4. Zeros of a Function Zeros are the x’s that make f(x) = 0 Find the zero of the function f(x) = x3 -4x2 + 2x - 8 How do you find them?

  5. Zeros of a Function Zeros are the x’s that make f(x) = 0 Find the zero of the function f(x) = x3 - 4x2 + 2x - 8 How do you find them? Factoring would work

  6. Group factoring f(x) = x3 -4x2 + 2x – 8 f(x) = x2(x - 4) + 2(x - 4)

  7. Group factoring f(x) = x3 -4x2 + 2x – 8 f(x) = x2(x - 4) + 2(x - 4) f(x) = (x – 4)(x2 + 2) 0 = (x – 4) and 0 = (x2 + 2), 4 = x - 2 = x2 thus the only real answer is x = 4

  8. We only worry about the numerator. 0 = 2a – 6 a = 3

  9. Increasing and Decreasing Function “Increasing” function x1<x2 implies f (x2)>f (x1) “Decreasing” functionx3<x4 implies f (x3)>f (x4) f(2)f(3) x1 x2 x3 x4

  10. Constant Function Here f(2)f(3) x1 x2 x3 x4

  11. Definition of Relative Minimum and Maximum Over a Given Interval Minimum is the lowest point Maximum is the highest point. This will lead to the “Extreme Value Theorem”

  12. Even and Odd Functions EVEN function is where f(x) = f(- x) Odd function is where f(- x) = - f(x) Let g(x) = x3 + x thus ( -x)3 + (- x) so - x3 – x ; - g(x) = - (x3 + x) It is then Odd f(x) = x4 + 2 thus f(-x) = (-x)4 + 2 ; x4 + 2 which is the same as f(x) It is then Even

  13. Homework Page 47-50 # 2, 10, 16, 22, 32, 54, 60, 62, 66, 86

  14. Homework Day 2 Page 47 – 50 #17, 23, 33, 37, 49, 55, 57, 61, 63, 83, 89

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