User:Tim Barsness/classes/calculus/section1.1/

Four Ways to Represent a Function[edit]

1.
a) f(-1) = -2
b) f(2) ~= 3.8
c) f(x) = 2 when x = 1 or x = -3
d) f(x) = 0 when x ~= -2.5 or x ~= .4
e) domain: -3 <= x <= 3  
   range: -2 <= y <= 3
f) f is increasing on the interval (-1,3)

2.
a) f(-4) = -2
   g(3) = 4
b) f(x) = g(x) when x = -2 and x = 2
c) f(x) = -1 when x ~= -3 or x ~= 4
d) f is decreasing on the interval (0,4)
e) domain of f: [-4, 4]
   range of f: [-2, 3]
f) domain of g: [-4, 3]
   range of g: [.5, 4]

3. Vertical ground acceleration range  $(cm/s^{2})$ : [-75, 125]
   East-West ground acceleration range  $(cm/s^{2})$ : [-200, 200]
   North-South ground acceleration range  $(cm/s^{2})$ : [-300, 450]

4. 1) My paycheck is a function of the amount of time I worked
   2) My test scores are a function of the amount of time spent studying
   3) The amount of time I spent studying is a function of the amount of time I wasted playing video games
   
   1) The domain of my paycheck is between 0 and 40 hours.  The range is from 0 to 400 dollars.  
   2) The domain of my test scores is between 0 and 1 hours spent studying (short attention span) and the range is between 0 and 
      100 percent.
   3) The domain of the amount of time I spent studying is from 0 to 80 hours playing video games.  The range of time spent 
      studying is from 0 to 1 hours.

5. Not a function of x because there is more than one y value for a single x value (it fails the vertical line test).

6. This function is a function of x.
   Domain: [-2, 2]
   Range: [0, 3]

7. This function is a function of x.
   Domain: [-3, 2]
   Range:  $[-3,2)\cup [-1,3]$ 

8. This is not a function of x because there is more than on y value for integer values of x (it fails the vertical line test).

9. As a general trend, the person is gaining weight over time.  They gain weight most rapidly in the first 20 years of their 
   life.  They went on a diet at age 30 and lost 20 and kept it off for 5 years.  When the person stopped dieting, they quicky 
   gained the weight back and continued their increasing weight trend into their 70's.