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 : [-75, 125]
East-West ground acceleration range : [-200, 200]
North-South ground acceleration range : [-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:
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.