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

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

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 x 1 and x 2 in the interval, x 1 < x 2 impliesf(x 1 ) < f(x 2 ) A function f is decreasing on an interval if, for any x 1 and x 2 in the interval, x 1 f(x 2 ) A function f is constant on an interval if, for any x 1 and x 2 in the interval, f(x 1 ) = f(x 2 ) 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) A function is y = f(x) is odd if, for each x in the domain of f, f(-x) = -f(x) An even function is symmetric about the y-axis. An odd function is symmetric about the origin.

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

7. Summary of Graphs of Common Functions f(x) = c y = x y = x 2 y = x 3

8. The Greatest Integer Function -4 -3 -2 -1 0 1 2 3 4 5 x y 0.2.5.8.99 0000000000 1 2 3 x y 1.1 1.4 1.7 1.8 1.99 1111111111

9. Average Rate of Change of a Function Find the average rates of change of f(x) = x 3 - 3x from x 1 = -2 to x 2 = 0. The average rate of change of f from x 1 to x 2

10. Finding Average Speed The average speed of s(t) from t 1 to t 2 is Ex. The distance (in feet) a moving car is from a stoplight is given by the function s(t) = 20t 3/2, where t is the time (in seconds). Find the average speed of the car from t 1 = 0 to t 2 = 4 seconds. What’s the average speed of the car from 4 to 9 seconds?