Key to In Class Exam 1 Review

1. a) b) c) d) (-3,3)

e)

2. max profit=$11,250 at quantity=2500 break even at 1000 or 4000 games.

3. f(x)= { .05x x < 20,000

{ .1(x-20000) + 1000 20000 < x

4. -7-12h

6. a) reflect across the x-axis, contract vertically by a factor of .02, shift right by 2000, and last shift up by 79000 units.

Vertex=(2000,79000) axis is x=2000, range is ( y-intercept is -1000

x-intercepts are approximately 3987.46 and 12.5393

b) expand vertically by a factor of 6, shift left by 1 unit and last shift down by 54 units.

Vertex=(-1,-54) axis is x=-1, range is [-54, y intercept is -48, x intercepts are

2 and -4.

c) The transformations of y=lnx which result in f(x) are shift left 2 units, expand vertically by a factor of 3 and last, shift up 7 units.

7. a) x int. = -1/25 y-int. = 1/6 V.A. x=4 and x=6 H.A. y=0

b) VA x=5 and x=1 HA y= -3

c) VA x=4 ( There is only a hole at (-2, ¾) ) HA y=3/2

8. a) b) c) 3 d) 0 .25 e) 47/8

9. a) doubling time = 7.87 years time to reach 4500 = 4.6 years

b) doubling time =7.7 years time to reach 4500 = 4.5 years

10. a) $32,969.78 b) $32,928.70 c) 7.29557281%

11. a) -1 b) 5 c) 3/2

12. a) at x= -2 and at x=2 A rational function is only not continuous where the denominator is equal to 0. ( even if it is just a hole at that x value)

b) All 3 pieces are continuous functions so we only need to check the x-values where the definition changes. At x= -1, the left side is -1. The right side is also -1 and the function value is -1 so the function is continuous at x= -1. At x=2, the left side is -4 but the right side is 5 so there is a gap/jump at x=2 and f is not continuous at x=2.

13 will not be on the exam

13 a) 0 b) 0

14. a) The data looks like a quadratic. Trying quadratic regression gives r^2 = 1

y=

b) This data looks like a cubic and we find r^2=1 with cubic regression

y=

c) The data looks exponential and exp regression gives r^2=1. y=