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1.5 Analyzing Graphs of Functions

1.5 Analyzing Graphs of Functions. (2,4). Find: the domain the range f(-1) = f(2) =. (4,0). [-1,4). [-5,4]. -5. (-1,-5). 4. Vertical Line Test for Functions. Do the graphs represent y as a function of x?. yes. yes. no. Increasing and Decreasing Functions.

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1.5 Analyzing Graphs of Functions

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  1. 1.5 Analyzing Graphs of Functions (2,4) • Find: • the domain • the range • f(-1) = • f(2) = (4,0) [-1,4) [-5,4] -5 (-1,-5) 4

  2. Vertical Line Test for Functions Do the graphs represent y as a function of x? yes yes no

  3. Increasing and Decreasing Functions -2 -1 1 2 3 4 5 1. The function is decreasing on the interval (-2,0). 2. The function is constant on the interval (0,3). 3. The function is increasing on the interval (3,5).

  4. A function f is increasing on an interval if, for any x1 and x2 in the interval, x1 < x2 implies f(x1) < f(x2) A function f is decreasing on an interval if, for any x1 and x2 in the interval, x1 < x2 implies f(x1) > f(x2) A function f is constant on an interval if, for any x1 and x2 in the interval, f(x1) = f(x2) go to page 57

  5. Tests for Even and Odd Functions A function is y = f(x) is even if, for each x in the domain of f, f(-x) = f(x) An even function is symmetric about the y-axis. A function is y = f(x) is odd if, for each x in the domain of f, f(-x) = -f(x) An odd function is symmetric about the origin.

  6. Ex. g(x) = x3 - x g(-x) = (-x)3 – (-x) = -x3 + x = -(x3 – x) Therefore, g(x) is odd because f(-x) = -f(x) Ex. h(x) = x2 + 1 h(-x) = (-x)2 + 1 = x2 + 1 h(x) is even because f(-x) = f(x)

  7. Summary of Graphs of Common Functions f(x) = c y = x y = x 3 y = x2

  8. The Greatest Integer Function -4 -3 -2 -1 0 1 2 3 4 5 x y x y 1.1 1.4 1.7 1.8 1.99 1 1 1 1 1 0 .2 .5 .8 .99 0 0 0 0 0 1 2 3

  9. Average Rate of Change of a Function Find the average rates of change of f(x) = x3 - 3x from x1 = -2 to x2 = 0. The average rate of change of f from x1 to x2

  10. Finding Average Speed The average speed of s(t) from t1 to t2 is Ex. The distance (in feet) a moving car is from a stoplight is given by the function s(t) = 20t3/2, where t is the time (in seconds). Find the average speed of the car from t1 = 0 to t2 = 4 seconds. What’s the average speed of the car from 4 to 9 seconds?

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