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

Four Ways to Represent a Function
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.